Document:

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                                                                    EXHIBIT 10.1

                      STOCK AND WARRANT PURCHASE AGREEMENT

Cardima, Inc.
47266 Benicia Street
Fremont, California 94538

Ladies & Gentlemen:

     The undersigned purchaser (the "Purchaser") hereby confirms its agreement
with you as follows:

     1.  This Stock and Warrant Purchase Agreement (the "Purchase Agreement") is
made by and between Cardima, Inc., a Delaware corporation (the "Company"), and
the Purchaser as of the date this Purchase Agreement is accepted by the Company
below (the "Effective Date").

     2.  This Purchase Agreement is one of a series of stock and warrant
purchase agreements of the Company relating to the offering (the "Offering") of
securities of the Company.  In connection with this Offering, the Company has
authorized the issuance and sale of up to a maximum aggregate number of fifteen
million (15,000,000) shares of the Company's Common Stock, par value $0.001 per
share (the "Common Stock"), and warrants to purchase up to seven million five
hundred thousand (7,500,000) shares of the Company's Common Stock (the
"Warrants").

     3.  The Company and the Purchaser agree that the Purchaser will purchase
from the Company, and the Company, conditioned upon acceptance in whole or in
part, will sell to the Purchaser  _________ shares of Common Stock, at a
purchase price per share of Common Stock equal to $0.58 (the "Purchase Price"),
and pursuant to, the Terms and Conditions for Purchase of Common Stock and
Warrants attached hereto as Annex I and incorporated herein by reference as if
fully set forth herein.

     4.  For every two (2) shares of Common Stock purchased by the Purchaser,
the Company will issue to the Purchaser, a Warrant to purchase one (1) share of
Common Stock.  The exercise price of the Warrant shall be $0.87.  Each Warrant
shall be exercisable commencing six (6) months after the date of issuance;
provided, that the number of Warrant Shares (as defined in Annex I hereto) shall
--------
be permanently reduced on a share-for-share basis to the extent that the
Purchaser sells Common Stock or other securities of the Company during such six
(6) month period.  The Warrants are redeemable by the Company at a price of
$0.001 per Warrant Share upon notice to record holders of the Warrants if the
average closing bid price of the Common Stock has been at least $1.16 for
fifteen (15) consecutive trading days during a period ending within five (5)
business days of the date of the notice of redemption, all as more fully
described in this Purchase Agreement, the Warrant and accompanying documents.
The Warrants are also subject to a mandatory exchange or termination in the case
of certain reorganizations, mergers, or divestitures.

     5.  The Common Stock and Warrants will be sold on a first come, first
served basis.  The Company makes no representation that this Purchase Agreement
will be accepted by the Company.  In its Offering of Common Stock and Warrants,
the Company may enter into Stock and Warrant Purchase Agreements with other
purchasers; such purchasers may hereinafter be referred to as the "Purchasers."

                                       1
<PAGE>

     6.  Purchaser hereby agrees not to engage, directly or indirectly, in any
short sale or third party short sales or hold a "put equivalent position" with
respect to the Common Stock for a thirty (30) day period prior to and for a one
hundred eighty (180) day period following the Closing Date.

     Please confirm that the foregoing correctly sets forth the agreement
between us by signing in the space provided below for that purpose.

                              PURCHASER

                              Print Name

                              By:
                                  _____________________________________

                              Title:
                                     __________________________________

                              Address:
                                       ________________________________

                                       ________________________________

                                       ________________________________

                              Facsimile No.:
                                             __________________________

                              Telephone No.:
                                             __________________________

ACCEPTED as of _____________, 2001

CARDIMA, INC., a Delaware Corporation

By:
    ____________________________________________
    Gabriel B. Vegh
    President and Chief Executive Officer

                                       2
<PAGE>

                                    ANNEX I

         TERMS AND CONDITIONS FOR PURCHASE OF COMMON STOCK AND WARRANTS

1.   Authorization and Sale of the Common Stock and Warrants.
     -------------------------------------------------------

     1.1  Authorization of the Common Stock and Warrants.  The Company has
          ----------------------------------------------
authorized the issuance and sale of up to fifteen million (15,000,000) shares of
the Company's Common Stock, par value $0.001 per share (the "Common Stock") and
warrants to purchase up to an aggregate of seven million five hundred thousand
(7,500,000) shares of the Company's Common Stock (the "Warrants") in the form
attached hereto as Exhibit 1.1.

     1.2  Sale of Common Stock and Warrants.  Subject to the terms and
          ---------------------------------
conditions hereof, the Purchaser will purchase the number of shares of Common
Stock and Warrants agreed upon by the Purchaser and accepted by the Company at
the Purchase Price, as set forth in the Stock and Warrant Purchase Agreement by
and between the Company and the Purchaser (the "Purchase Agreement").  The
shares of Common Stock sold to Purchaser pursuant to the Purchase Agreement are
hereinafter referred to as the "Initial Shares" and the shares of Common Stock
arising from the exercise of the Warrant are hereinafter referred to as the
"Warrant Shares." The Initial Shares, the Warrant and the Warrant Shares are
hereinafter collectively referred to as the "Securities."

2.   Closings.
     --------

     2.1  Closing Date.  One or more closings of the purchase and sale of the
          ------------
Common Stock and Warrants in the Offering hereunder (the "Closing") shall be
held at such place and such times as the Company may select.  Each date of a
Closing of the purchase or sale of the Common Stock and Warrants in connection
with the Offering is hereinafter referred to as a "Closing Date."  As of the
Closing Date for a specific purchase of Common Stock and Warrants, the Company
shall prepare a certificate or certificates registered in the name of the
Purchaser representing the Initial Shares to be purchased by such Purchaser
under the Purchase Agreement, and the Purchaser shall send to the Company a wire
transfer (in accordance with the instructions set forth on Exhibit 2.1 hereto)
in the amount of the Purchase Price of the shares of Common Stock to be
purchased by such Purchaser, payable to the Company's order.  Funds received
prior to the Closing Date will not bear interest.

     2.2  Warrant Issuance.  The Company will issue a Warrant to purchase one
          ----------------
(1) share of the Company's Common Stock at a per share exercise price of
$[___][which shall be 150% of Purchase Price] to each Purchaser for every two
(2) shares of the Company's Common Stock purchased by the Purchaser at the
Closing.  The Warrant will be issued as of the Closing and the Company shall
deliver the Warrant to the Purchaser as promptly as practicable after the
Closing Date; provided, however, that the Purchaser may not exercise the Warrant
              --------  -------
until six (6) months after the Closing (the "Warrant Determination Date").  The
number of Warrant Shares will be permanently reduced on a share-for-share basis
by any sales of Company securities (including short sales and sales or purchases
of derivative securities) by the Purchaser from the Closing Date until the
Warrant Determination Date.  As a condition to exercising the Warrant, the
Purchaser shall provide to the Company an affidavit and other reasonable
supporting materials stating the amount of Company securities sold (including
short sales and sales or purchase of derivative securities) from the Closing
Date to the Warrant Determination Date.  The Warrant is redeemable by the
Company at a price of $0.001 per Warrant Share upon notice to the record holder
of the Warrant if the average closing price per share of the Common Stock as
reported by the National Association of Securities Dealers Automated Quotations
("NASDAQ") or the OTC Bulletin Board has been at least $____ [which shall be
200% of the Purchase Price] for a period of fifteen (15) consecutive trading
days ending within five (5) business days of the date of

                                   Annex 1-1
<PAGE>

the notice of redemption. The Warrant is also subject to a mandatory exchange or
termination in the case of certain reorganizations, mergers, or divestitures.

3.   Representations and Warranties of the Company.  The Company represents and
     ---------------------------------------------
warrants to the Purchaser as of the Closing Date as follows, except as set forth
in the SEC Documents (as defined below):

     3.1  Organization and Standing.  The Company is a corporation organized,
          -------------------------
validly existing and in good standing under the laws of the State of Delaware
and has the requisite corporate power and authority to own or lease its
properties and conduct its businesses as it is now being conducted.

     3.2  Corporate Power; Authorization.  The Company has all requisite legal
          ------------------------------
and corporate power and has taken all requisite corporate action to execute and
deliver the Purchase Agreement, to sell and issue the Securities and to carry
out and perform all of its obligations hereunder.  The Purchase Agreement has
been duly authorized, executed and delivered on behalf of the Company and
constitutes the valid and binding agreement of the Company, enforceable in
accordance with its terms, except (i) as limited by applicable bankruptcy,
insolvency, reorganization or similar laws relating to or affecting the
enforcement of creditors' rights generally, (ii) as limited by equitable
principles generally and (iii) rights to indemnification hereunder may be
limited by applicable law.

     3.3  Validity of Securities.  The Company has full corporate power and
          ----------------------
lawful authority to sell the Securities on the terms and conditions contemplated
herein, and when so sold against payment therefor as provided herein and in the
Warrant, the Initial Shares and, when issued, the Warrant will be validly
authorized and issued, fully paid and nonassessable.  The issuance and delivery
of each of the Initial Shares and the Warrant is not subject to preemptive or
any similar rights of the stockholders of the Company or any liens or
encumbrances arising through the Company and when the Warrant Shares are issued
in accordance with the terms of the Warrant, they will be validly issued and
outstanding, fully paid and nonassessable.

     3.4  SEC Documents; Financial Statements.  The Company's Annual Report on
          -----------------------------------
Form 10-K for the fiscal year ended December 31, 2000 and the Company's most
recent Proxy Statement and Notice of Annual Stockholders' Meeting (the "SEC
Documents"), in each case as filed by the Company with the Securities and
Exchange Commission (the "SEC") have been made available to the Purchaser.  The
SEC Documents conform in all material respects to the requirements of the
Securities Exchange Act of 1934, as amended (the "Exchange Act"), as applicable,
and the rules, regulations and instructions of the SEC thereunder.  The SEC
Documents did not as of their dates contain any untrue statement of a material
fact or omit to state a material fact required to be stated therein or necessary
to make the statements made therein, in light of the circumstances in which they
were made, not misleading.  The financial statements of the Company included in
the SEC Documents (the "Financial Statements") comply as to form in all material
respects with applicable accounting requirements and with the published rules
and regulations of the SEC with respect thereto.  Except as may be indicated in
the notes to the Financial Statements, the Financial Statements have been
prepared in accordance with generally accepted accounting principles
consistently applied and fairly present, in all material respects, the financial
position of the Company at the dates thereof and the results of its operations,
stockholders' equity and cash flows for the periods then ended (subject, in the
case of unaudited statements, to normal, recurring adjustments).

     3.5  Subsequent Events.  Except as set forth in the press releases of the
          -----------------
Company, as publicly filed, since December 31, 2000, (i) the Company has not
incurred any liabilities or obligations, contingent or otherwise, that are
material in the aggregate to the Company taken as a whole, except in the
ordinary course of business, and (ii) there has been no material adverse change
in the condition or results of operations, financial or otherwise, of the
Company, taken as a whole.

                                   Annex 1-2
<PAGE>

     3.6  Legal Proceedings.  Except as set forth in the press releases of the
          -----------------
Company, as publicly filed, there are no material legal proceedings to which the
Company is a party or of which property of the Company is the subject and, to
the Company's knowledge, no such proceedings are contemplated by governmental
authorities or others.

     3.7  Approvals.  Subject to compliance with the provisions of applicable
          ---------
securities laws of state or foreign jurisdictions, no other approval of any
public body (state or federal) is or will, on the Closing Date be necessary in
connection with the offer, issue and sale of the Initial Shares and the Warrant
as contemplated herein.

     3.8  No Breach.  The consummation of the transactions contemplated in the
          ---------
Purchase Agreement and the fulfillment of the terms thereof will not result in
(i) a violation of the Company's Amended and Restated Certificate of
Incorporation or Bylaws, (ii) a breach of any of the material terms or
provisions of, or constitute a default under, any material indenture, mortgage,
deed of trust or other agreement or instrument to which the Company is a party
or by which it is bound or (iii) a violation of any law, rule, regulation,
order, judgment or decree applicable to the Company or by which any property or
asset of the Company is bound.

     3.9  Licenses and Consents.  To the knowledge of the Company, the Company
          ---------------------
is in possession of and operating in compliance with all authorizations,
licenses, certificates, consents, orders and permits from state, federal and
other governmental authorities that are material to the conduct of its business,
all of which are valid and in full force and effect, except to the extent that
the failure to have or be in compliance with such is not reasonably likely to
have a material adverse effect on the Company's business or results from
operations.

     3.9  Outstanding Stock.  All outstanding shares of capital stock of the
          -----------------
Company have been duly authorized and validly issued and are fully paid and
nonassessable.

     3.10  Private Placement.  The Company has not taken any action inconsistent
           -----------------
with the treatment of the sale of the Common Stock and Warrants pursuant to the
Purchase Agreement as a private placement exempt from the registration
requirements of the Securities Act of 1933, as amended (the "Securities Act")
pursuant to the provisions of Section 4(2) thereof and Regulation D thereunder.
Assuming the accuracy of each Purchaser's representations and warranties in each
Purchaser's Purchase Agreement and the compliance by each Purchaser and AmeriCal
Securities, Inc., as placement agent in connection with the Offering, with all
of its covenants and agreements, the offer, sale, and issuance by the Company of
the Common Stock and Warrants to the Purchasers as contemplated herein
constitute transactions exempt from the registration requirements of Section 5
of the Securities Act.

     3.11  Use of Proceeds.  The Company intends to use the proceeds of the
           ---------------
Offering for working capital, including, without limitation, in connection with
the Company's Phase III trial for the treatment of atrial fibrilation and the
Company's efforts to obtain FDA approval for its microcatheter currently in
Phase III trial, and for such other purposes as the Company's Board of Directors
may determine from time to time.

4.   Representations and Warranties of the Purchaser; Access to Information;
     -----------------------------------------------------------------------
Independent Investigation.  The Purchaser hereby represents and warrants to the
-------------------------
Company as follows:

     4.1  Investment Intent.  The Purchaser is purchasing the Common Stock and
          -----------------
Warrants for investment for its own account only, not as a nominee or agent, and
not with a view to, or for resale in connection with, any "distribution" of any
part thereof within the meaning of the Securities Act.  The Purchaser has no
present intention of selling, granting any participation in, or otherwise
distributing the same.  The Purchaser does not have any contract, undertaking,
agreement or arrangement with any person to sell, transfer or grant any
participation to such person or to any third person with respect to any of the
Securities.

                                   Annex 1-3
<PAGE>

The Purchaser understands that the Securities have not been registered under the
Securities Act or registered or qualified under any state securities law in
reliance on specific exemptions therefrom, which exemptions may depend upon,
among other things, the bona fide nature of Purchaser's investment intent as
expressed herein. The Purchaser further understands that neither the Company nor
any of its officers or directors has any obligation to register the Securities
under any federal or state securities act or law, except as otherwise expressly
set forth in Section 5 hereof.

     4.2  Investment Experience.  The Purchaser is an "accredited investor"
          ---------------------
within the meaning of Rule 501 of the SEC, promulgated under the Securities Act,
and was not organized for the specific purpose of acquiring the Securities.  The
Purchaser had access to the SEC Documents and has carefully reviewed the
information contained therein, including, but not limited to, the section
entitled "Risks Affecting Future Results."  The Purchaser is aware of the
Company's business affairs and financial condition and has acquired sufficient
information about the Company to reach an informed and knowledgeable decision to
acquire the Securities.  The Purchaser has such business and financial
experience as is required to give it the capacity to protect its own interests
in connection with the purchase of the Securities.

     4.3  Authorization.  The Purchaser has full right, power and authority to
          -------------
enter into this Purchase Agreement and perform its obligations thereunder.  This
Purchase Agreement has been duly and validly authorized, executed and delivered
on behalf of the Purchaser and is a valid and binding agreement of the Purchaser
enforceable in accordance with its terms, subject as to enforceability to
general principles of equity and to bankruptcy, insolvency, moratorium and other
similar laws affecting the enforcement of creditors' rights generally.

     4.4  Compliance with Securities Laws and Regulations.  All subsequent
          -----------------------------------------------
offers and sales of the Securities by the Purchaser shall be made pursuant to
registration under the Securities Act and qualification under the applicable
state securities laws or pursuant to exemptions from registration and
qualification as well as compliance with the provisions of Section 5.1 below.

     4.5  Reliance by Company.  The Purchaser understands that the Securities
          -------------------
are being offered and sold to it in reliance on specific exemptions from the
registration and qualification requirements of United States federal and state
securities laws and that the Company is relying upon the truth and accuracy of,
and the Purchaser's compliance with the representations, warranties, agreements,
acknowledgments and understandings of the Purchaser set forth herein in order to
determine the availability of such exemptions and the eligibility of the
Purchaser to acquire the Securities.

     4.6  No Government Approval.  The Purchaser understands that no United
          ----------------------
States federal or state agency or any other government or governmental agency
has passed on or made any recommendation or endorsement of the Securities.

     4.7  No Legal, Tax or Investment Advice.  The Purchaser understands that
          ----------------------------------
nothing in the Purchase Agreement or any other materials presented to the
Purchaser in connection with the purchase and sale of the Securities constitutes
legal, tax or investment advice.  The Purchaser has consulted such legal, tax
and investment advisors as it, in its sole discretion, has deemed necessary or
appropriate in connection with its purchase of the Securities.

     4.8  Access to Information.  The Purchaser acknowledges that it has had the
          ---------------------
opportunity to ask questions, to receive answers concerning the Company and the
terms and conditions of the Offering from the Company and to obtain any
additional information from the Company that the Company possesses or can
acquire without unreasonable effort or expense regarding this Offering,
including, without limitation, information relating to the engagement of
AmeriCal Securities, Inc., as placement agent for the Offering pursuant to that
certain fee engagement letter agreement, dated April 10, 2001, which sets forth
the cash fees, warrants, and other arrangements in connection with the Offering.
In addition, the Purchaser acknowledges

                                   Annex 1-4
<PAGE>

that no private placement memorandum or similar document has been prepared in
connection with the Offering and the Company has not made any representations or
warranties other than as specifically set forth herein.

     4.9  Accredited Investor.  Purchaser makes the additional representations
          -------------------
and warranties set forth on Exhibit 4.9 attached hereto.

     4.10  Risk and Suitability.  The Purchaser acknowledges and realizes that
           --------------------
Purchaser's purchase of the Securities involves a high degree of risk and the
Purchaser could lose a substantial portion or all of its investment in the
Securities.  In addition, the Purchaser has such knowledge and experience in
business and financial matters, including without limitation, investment in
technology and biotechnology companies, as will enable the Purchaser to fend for
itself, bear the economic risk of its investment and evaluate the merits and
risks of an investment in the Securities and to make an informed investment
decision.  The Purchaser understands that the Company anticipates, based on
currently proposed plans and assumptions relating to its operations, that the
proceeds of this Offering will provide sufficient working capital to meet the
Company's needs in the near term.  In the event that the Company's plans change
or its assumptions change or prove to be inaccurate, the Company would be
required to seek additional financing sooner than anticipated.  There can be no
assurance that the Company will achieve cash flow from operations sufficient to
satisfy its working capital requirements, or at all, or that additional
financing will be available to the Company on commercially reasonable terms, or
at all.

     4.11  Threatened NASDAQ Delisting.  The Purchaser acknowledges and realizes
           ---------------------------
that while the Common Stock is currently listed on the NASDAQ SmallCap Market,
NASDAQ notified the Company, in a letter dated March 30, 2001, that the Company
had not met the requirements for continued listing on the NASDAQ SmallCap
Market, due to the fact that the Common Stock had been trading at less than
$1.00 since November 16, 2000, and that as of April 9, 2001, the Common Stock
would be delisted from the SmallCap Market.  The Company appealed this decision
and the Common Stock will remain listed on the NASDAQ SmallCap Market until
resolution of the appeal, which will be heard on May 18, 2001.  While the
Company believes that it is pursuing appropriate measures, such as a possible
reverse stock split, and can demonstrate to NASDAQ that it can sustain a trading
price above $1.00 per share, the NASDAQ appeal panel may not agree and may
delist the Common Stock.  If the Common Stock is delisted, the Company expects
that the Common Stock will be traded on the OTC Bulletin Board.

     4.12  Restricted Securities.  The Purchaser understands that the Securities
           ---------------------
it is purchasing are characterized as "restricted securities" under the federal
securities laws inasmuch as they are being acquired from the Company in a
transaction not involving a public offering and that under such laws and
applicable regulations such securities may be resold without registration under
the Securities Act only in certain limited circumstances.  In this connection,
the Purchaser represents that it is familiar with Rule 144 promulgated by the
SEC under the Securities Act, as presently in effect, and understands the resale
limitations imposed thereby and by the Securities Act.

5.   Restrictions on Transfer, Information and Registration Rights.
     -------------------------------------------------------------

     5.1  Restrictions on Transferability.  The Securities shall not be
          -------------------------------
transferable in the absence of a registration under the Securities Act or an
exemption therefrom, or in the absence of compliance with any term of the
Purchase Agreement.  Without limiting the foregoing, (i) the Securities may be
offered, resold, pledged or otherwise transferred only (A) in a transaction
meeting the requirements of Rule 144 of the SEC ("Rule 144"), or in accordance
with another exemption from the registration requirements of the Securities Act
(and based upon an opinion of counsel if the Company so requests) or (B)
pursuant to an effective registration statement under the Securities Act, in
each case in accordance with the applicable securities laws of any state of the
United States or any other applicable jurisdiction and (ii) Purchaser will be
required to notify any subsequent purchaser of the resale restrictions set forth
above.  The Company shall be entitled to

                                   Annex 1-5
<PAGE>

give stop transfer instructions to the transfer agent with respect to the
Securities in order to enforce the foregoing restrictions.

     5.2  Restrictive Legends.  Each certificate representing any of the
          -------------------
Securities shall bear substantially the following legends (in addition to any
legends required under applicable securities laws):

     THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE BEEN ACQUIRED FOR
     INVESTMENT AND HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933,
     AS AMENDED (THE "SECURITIES ACT").  THE SECURITIES MAY NOT BE SOLD,
     TRANSFERRED, ASSIGNED OR HYPOTHECATED UNLESS REGISTERED UNDER THE
     SECURITIES ACT AND QUALIFIED UNDER APPLICABLE STATE SECURITIES LAWS OR
     UNLESS SUCH SALE, TRANSFER, ASSIGNMENT OR HYPOTHECATION IS EXEMPT FROM THE
     REGISTRATION REQUIREMENTS OF THE SECURITIES ACT AND THE QUALIFICATION
     REQUIREMENTS OF APPLICABLE STATE SECURITIES LAWS AND THE COMPANY RECEIVES
     AN OPINION OF COUNSEL SATISFACTORY TO THE COMPANY THAT SUCH REGISTRATION
     AND QUALIFICATION ARE NOT REQUIRED.  THE SECURITIES REPRESENTED BY THIS
     CERTIFICATE AND THE RIGHTS OF HOLDERS THEREOF ARE SUBJECT TO CERTAIN
     RESTRICTIONS ON TRANSFER AND OTHER RESTRICTIONS, AND THE HOLDER OF THE
     SECURITIES REPRESENTED BY THIS CERTIFICATE (INCLUDING ANY FUTURE HOLDERS)
     IS BOUND BY THE TERMS OF A STOCK AND WARRANT PURCHASE AGREEMENT BETWEEN THE
     ORIGINAL PURCHASER AND THE COMPANY (COPIES OF WHICH MAY BE OBTAINED FROM
     THE COMPANY).

     5.3  Registration on Form S-3.
          ------------------------

          5.3.1  Filing of Registration Statement.  The Company shall use its
                 --------------------------------
best efforts to secure effectiveness of, as soon as practicable, and shall file
no later than forty-five (45) business days after the Closing Date (unless such
registration is not permitted under the applicable rules and regulations of the
SEC, a registration statement on Form S-3 (the "Registration Statement") with
the SEC pursuant to the Securities Act to register the resale of the Initial
Shares and Warrant Shares (the "Registrable Securities"); provided however, that
                                                          -------- -------
in the event the Company fails (due to an action or inaction of the Company) to
be eligible to file a registration statement on Form S-3, the Company shall file
with the SEC pursuant to the Securities Act a registration statement on Form S-
1.

          5.3.2  Registration Expenses.  The Company shall pay all Registration
                 ---------------------
Expenses (as defined below) in connection with any registration, qualification
or compliance hereunder, and each holder of Registrable Securities (a "Holder;"
collectively, the "Holders") shall pay all Selling Expenses related to such
Holder's sale of Registrable Securities (as defined below) and other expenses
that are not Registration Expenses relating to the Registrable Securities resold
by such Holder.  "Registration Expenses" shall mean all expenses, except for
Selling Expenses, incurred by the Company in complying with the registration
provisions herein described, including, without limitation, all registration,
qualification and filing fees, printing expenses, fees and disbursements of
counsel for the Company, blue sky fees and expenses and the expense of any
special audits incident to or required by any such registration.  "Selling
Expenses" shall mean all selling commissions, underwriting fees and stock
transfer taxes applicable to the Registrable Securities and all fees and
disbursements of counsel for any Holder.

          5.3.3  Additional Company Obligations.  In the case of any
                 ------------------------------
registration effected by the Company pursuant to these registration provisions,
the Company will use its best efforts to: (i) keep such registration effective
until two years after the Closing Date (or such earlier date as all of the
Registrable Securities have been sold or may be sold under Rule 144(k)); (ii)
prepare and file with the SEC such amendments and supplements to the
Registration Statement and the prospectus used in connection with the

                                   Annex 1-6
<PAGE>

Registration Statement as may be necessary to comply with the provisions of the
Securities Act with respect to the disposition of the Registrable Securities;
(iii) furnish such number of prospectuses and other documents incident thereto,
including any amendment of or supplement to the prospectus, as a Holder from
time to time may reasonably request; (iv) cause all such Registrable Securities
registered as described herein to be listed on each securities exchange and
quoted on each quotation service on which similar securities issued by the
Company are then listed or quoted; (v) provide a transfer agent and registrar
for all Registrable Securities registered pursuant to the Registration Statement
and a CUSIP number for all such Registrable Securities; (vi) use its reasonable
efforts to comply with all applicable rules and regulations of the SEC and (vii)
notify Holders of the happening of any event as a result of which the prospectus
included in the Registration Statement, as then in effect, includes an untrue
statement of a material fact or omits to state a material fact required to be
stated therein or necessary to make the statements therein not misleading in
light of the circumstances then existing; and (viii) file the documents required
of the Company and otherwise use its best efforts to maintain requisite blue sky
clearance in (A) all jurisdictions in which any of the Registrable Securities
are originally sold and (B) all other states specified in writing by a Holder as
may reasonably be required to sell such Holder's Registrable Securities,
provided as to clause (B), however, that the Company shall not be required to
qualify to do business or consent to service of process in any state in which it
is not now so qualified or has not so consented.

          5.3.4  Providing Information.  Each Holder of Registrable Securities
                 ---------------------
shall furnish to the Company such information regarding such Holder and the
distribution proposed by such Holder as the Company may reasonably request in
writing and as shall be reasonably required in connection with any registration,
qualification or compliance described herein.  Such Holder shall represent that
such information is true and complete.

          5.3.5  Limitations on Sale.  The Company may at any time refuse to
                 -------------------
permit the Holders to resell any Registrable Securities pursuant to the
Registration Statement; provided, however, that in order to exercise this right,
the Company must deliver a certificate in writing to the Holders to the effect
that a delay in such sales is necessary because, in the good faith judgment of
the Company, sales pursuant to the Registration Statement would require the
public disclosure of information that would not otherwise be required to be
disclosed (which disclosure would, in the good faith judgment of the Company,
have a significant adverse effect on the Company) or could in other respects
constitute a violation of the federal securities laws or otherwise materially
adversely affect the Company.  In such an event, the Company shall notify the
Holders promptly after it has determined that such circumstances no longer
exist.  The Company shall not under any circumstances be entitled to refuse to
permit the Holders to resell any Registrable Securities under this Section (i)
more than two (2) times in the twelve (12) month period following the Closing
Date, and any individual period during which the Company refuses to permit the
Holder to resell any Registrable Securities in the twelve (12) month period
following the Closing Date shall not exceed sixty (60) days, and (ii) more than
two (2) times in the second twelve month period following the Closing Date, and
any Registrable Securities in the second twelve (12) month period following the
Closing Date shall not exceed forty-five (45) days.  Each Purchaser hereby
covenants and agrees that it will not sell any Registrable Securities pursuant
to the Registration Statement during the periods the Company refuses to permit
the Holder to resell any Registrable Securities as set forth in this Section.

     5.4  Indemnification and Contribution.
          --------------------------------

          5.4.1  Indemnification by the Company.  The Company agrees to
                 ------------------------------
indemnify and hold harmless each Holder from and against any losses, claims,
damages or liabilities (or actions or proceedings in respect thereof) to which
such Holder may become subject (under the Securities Act or otherwise) insofar
as such losses, claims, damages or liabilities (or actions or proceedings in
respect thereof) arise out of, or are based upon, any claim by a third party
asserting any untrue statement of a material fact contained in the Registration
Statement, on the effective date thereof, or arise out of any failure by the
Company to fulfill any undertaking included in the Registration Statement, and
the Company will, as incurred, reimburse such

                                   Annex 1-7
<PAGE>

Holder for any legal or other expenses reasonably incurred in investigating,
defending or preparing to defend any such action, proceeding or claim; provided,
                                                                       --------
however, that the Company shall not be liable in any such case to the extent
-------
that such loss, claim, damages or liability arises out of, or is based upon (i)
an untrue statement or alleged untrue statement made in such Registration
Statement in reliance upon and in conformity with written information furnished
to the Company by or on behalf of such Holder specifically for use in
preparation of the Registration Statement or (ii)) any untrue statement in any
prospectus that is corrected in any subsequent prospectus that was delivered to
the Holder prior to the pertinent sale or sales by the Holder.

          5.4.2  Indemnification by Holder.  Each Holder, severally and not
                 -------------------------
jointly, agrees to indemnify and hold harmless the Company from and against any
losses, claims, damages or liabilities (or actions or proceedings in respect
thereof) to which the Company may become subject (under the Securities Act or
otherwise) insofar as such losses, claims, damages or liabilities (or actions or
proceedings in respect thereof) arise out of, or are based upon any claim by a
third party asserting (i) an untrue statement made in such Registration
Statement in reliance upon and in conformity with written information furnished
to the Company by or on behalf of such Holder specifically for use in
preparation of the Registration Statement, provided, however, that no Holder
                                           --------  -------
shall be liable in any such case for any untrue statement included in any
Prospectus which statement has been corrected, in writing, by such Holder and
delivered to the Company at least three business days before the sale from which
such loss occurred or (ii) any untrue statement in any prospectus that is
corrected in any subsequent prospectus that was delivered to the Holder prior to
the pertinent sale or sales by the Holder, and each Holder, severally and not
jointly, will, as incurred, reimburse the Company for any legal or other
expenses reasonably incurred in investigating, defending or preparing to defend
any such action, proceeding or claim.

          5.4.3  Indemnification Procedures.  Promptly after receipt by any
                 --------------------------
indemnified person of a notice of a claim or the beginning of any action in
respect of which indemnity is to be sought against an indemnifying person
pursuant to this Section 5.4, such indemnified person shall notify the
indemnifying person in writing of such claim or of the commencement of such
action, and, subject to the provisions hereinafter stated, in case any such
action shall be brought against an indemnified person and the indemnifying
person shall have been notified thereof, the indemnifying person shall be
entitled to participate therein, and, to the extent that it shall wish, to
assume the defense thereof, with counsel reasonably satisfactory to the
indemnified person; provided, however, that the failure of any indemnified party
                    --------  -------
to give notice as provided herein shall not relieve the indemnifying party of
its obligations hereunder unless the failure to give such notice is materially
prejudicial to an indemnifying party's ability to defend such action.  After
notice from the indemnifying person to such indemnified person of the
indemnifying person's election to assume the defense thereof, the indemnifying
person shall not be liable to such indemnified person for any legal expenses
subsequently incurred by such indemnified person in connection with the defense
thereof; provided, however, that if there exists or shall exist a conflict of
         --------  -------
interest that would make it inappropriate in the reasonable opinion of counsel
for the indemnified person for the same counsel to represent both the
indemnified person and such indemnifying person or any affiliate or associate
thereof, the indemnified person shall be entitled to retain its own counsel at
the expense of such indemnifying person; provided, however, that in the case of
                                         --------  -------
the immediately preceding proviso the indemnifying person shall not be
responsible for the legal expenses of more than one counsel for all indemnified
persons.

          5.4.4  Contribution in Lieu of Indemnity.  If the indemnification
                 ---------------------------------
provided for in this Section 5.4 is unavailable to or insufficient to hold
harmless an indemnified party under Section 5.4.1 or 5.4.2 above in respect of
any losses, claims, damages or liabilities (or actions or proceedings in respect
thereof) referred to therein, then each indemnifying party shall contribute to
the amount paid or payable by such indemnified party as result of such losses,
claims, damages or liabilities (or actions in respect thereof), as well as any
other relevant equitable considerations.  The relative fault shall be determined
by reference to, among other things, whether the untrue or alleged untrue
statement of a material fact or the omission or alleged omission to state a
material fact relates to information supplied by the Company on the one hand or
a Holder

                                   Annex 1-8
<PAGE>

on the other and the parties' relative intent, knowledge, access to information
and opportunity to correct or prevent such statement or omission. The Company
and the Holders agree that it would not be just and equitable if contribution
pursuant to this Section 5.4.4 were determined by pro rata allocation (even if
the Holders were treated as one entity for such purpose) or by any other method
of allocation which does not take account of the equitable considerations
referred to above in this Section 5.4.4. The amount paid or payable by an
indemnified party as a result of the losses, claims, damages or liabilities (or
actions in respect thereof) referred to above in this Section 5.4.4 shall be
deemed to include any legal or other expenses reasonably incurred by such
indemnified party in connection with investigating or defending any such action
or claim. Notwithstanding the provisions of this Section 5.4.4, no Holder shall
be required to contribute any amount in excess of the net amount received by the
Holder from the sale of the Registrable Securities to which such loss relates.
No person guilty of fraudulent misrepresentation (within the meaning of Section
11 (f) of the Securities Act) shall be entitled to contribution from any person
who was not guilty of such fraudulent misrepresentation. The Holders'
obligations in this Section 5.4.4 to contribute are several in proportion to
their respective sales of Registrable Securities to which such loss relates and
not joint.

          5.4.5  Controlling Persons Indemnified.  The obligations of the
                 -------------------------------
Company and the Holders under this Section 5.4 shall be in addition to any
liability which the Company and the respective Holders may otherwise have and
shall extend, upon the same terms and conditions, to each person, if any, who
controls the Company or any Holder within the meaning of the Securities Act.

     5.5  Reports Under the Exchange Act.  With a view to make available to the
          ------------------------------
Purchasers or Holders the benefits of Rule 144 promulgated under the Securities
Act and any other rule or regulation of the SEC that may at any time permit a
Purchaser or Holder to sell Securities to the public without registration or
pursuant to a registration on Form S-3, the Company will covenant and agree to:
(i) make and keep public information available, as those terms are understood
and defined in Rule 144, at all times after the Closing; (ii) file with the SEC
in a timely manner all reports and other documents required of the Company under
the Securities Act and the Exchange Act; and (iii) furnish to any Purchaser or
Holder, so long as the Purchaser or Holder owns any Securities forthwith upon
request, (A) a written statement by the Company that it has complied with the
reporting requirements of Rule 144, the Securities Act and the Exchange Act, (B)
a copy of the most recent annual or quarterly report of the Company, and (C)
such other information as may be reasonably requested in order to avail any
Purchaser or Holder of any rule or regulation of the SEC that permits the
selling of any such Securities without registration or pursuant to such Form S-
3.

6.   Miscellaneous.
     -------------

     6.1  Waivers and Amendments.  Without the written consent of (i) the
          ----------------------
Company, and the record holders of more than fifty percent (50%) of the
Securities issued to the Purchasers (on a converted-to-Common Stock basis) then
outstanding that have not previously been sold in a public offering, the terms
of the Purchase Agreement may not be waived or amended.

     6.2  Governing Law.  The Purchase Agreement shall be governed in all
          -------------
respects by the laws of the State of California as such laws are applied to
agreements between California residents entered into and to be performed
entirely within California.  The Purchaser hereby irrevocably submits to the
jurisdiction of any State or United States Federal court sitting in Alameda or
San Francisco counties in the State of California over any action or proceeding
arising out of or relating to this Purchase Agreement or any agreement
contemplated hereby, and the Purchaser hereby irrevocably agrees that all claims
in respect of such action or proceeding may be heard and determined in such
State or Federal court.  The Purchaser further waives any objection to venue in
such State and any objection to an action or proceeding in such State on the
basis of a non-convenient forum.  The Purchaser further agrees that any action
or proceeding brought against the Company shall be brought only in the State or
United States Federal courts sitting in Alameda or San Francisco counties in the
State of California.  THE PURCHASER AGREES TO WAIVE ITS RIGHT TO A JURY TRIAL ON
ANY CLAIM OR CAUSE OF ACTION BASED UPON OR ARISING OUT OF

                                   Annex 1-9
<PAGE>

THIS PURCHASE AGREEMENT OR ANY DOCUMENT OR AGREEMENT CONTEMPLATED HEREBY.

     6.3  Survival.  The representations, warranties, covenants and agreements
          --------
made herein shall survive any investigation made by the Company or the Purchaser
and the Closing.

     6.4  Successors and Assigns.  Subject to Section 5, the provisions hereof
          ----------------------
shall inure to the benefit of, and be binding upon, the successors, assigns,
heirs, executors and administrators of the parties hereto (specifically
including successors in interest to the Securities).

     6.5  Entire Agreement.  The Purchase Agreement (including all Exhibits
          ----------------
thereto) constitutes the full and entire understanding and agreement between the
parties with regard to the subject hereof.

     6.6  Notices, etc.  All notices and other communications required or
          -------------
permitted hereunder shall be effective upon receipt and shall be in writing and
may be delivered in person, by facsimile, or express delivery service, addressed
(a) if to the Purchaser, at the address set forth on the signature page hereof
or at such other address as the Purchaser shall have furnished the Company in
writing, or (b) if to the Company, at its address set forth at the beginning of
the Purchase Agreement, or at such other address as the Company shall have
furnished to the Purchaser in writing.

     6.7  Severability.  If any provision of the Purchase Agreement shall be
          ------------
judicially determined to be invalid, illegal or unenforceable, the validity,
legality and enforceability of the remaining provisions shall not in any way be
affected or impaired thereby.

     6.8  Titles and Subtitles.  The titles of the paragraphs and subparagraphs
          --------------------
of the Purchase Agreement are for convenience of reference and shall not, by
themselves, determine the construction of the Purchase Agreement.

     6.9  Counterparts.  The Purchase Agreement may be executed in any number of
          ------------
counterparts, each of which be an original, but all of which together shall
constitute one instrument.

                                  Annex 1-10
<PAGE>

                                                                     Exhibit 1.1
                                                                     -----------

Warrant No. _______________

     THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE BEEN ACQUIRED FOR
     INVESTMENT AND HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933,
     AS AMENDED (THE "SECURITIES ACT").  THE SECURITIES MAY NOT BE SOLD,
     TRANSFERRED, ASSIGNED OR HYPOTHECATED UNLESS REGISTERED UNDER THE
     SECURITIES ACT AND QUALIFIED UNDER APPLICABLE STATE SECURITIES LAWS OR
     UNLESS SUCH SALE, TRANSFER, ASSIGNMENT OR HYPOTHECATION IS EXEMPT FROM THE
     REGISTRATION REQUIREMENTS OF THE SECURITIES ACT AND THE QUALIFICATION
     REQUIREMENTS OF APPLICABLE STATE SECURITIES LAWS AND THE COMPANY RECEIVES
     AN OPINION OF COUNSEL SATISFACTORY TO THE COMPANY THAT SUCH REGISTRATION
     AND QUALIFICATION ARE NOT REQUIRED.  THE SECURITIES REPRESENTED BY THIS
     CERTIFICATE AND THE RIGHTS OF HOLDERS THEREOF ARE SUBJECT TO CERTAIN
     RESTRICTIONS ON TRANSFER AND OTHER RESTRICTIONS, AND THE HOLDER OF THE
     SECURITIES REPRESENTED BY THIS CERTIFICATE (INCLUDING ANY FUTURE HOLDERS)
     IS BOUND BY THE TERMS OF A STOCK AND WARRANT PURCHASE AGREEMENT BETWEEN THE
     ORIGINAL PURCHASER AND THE COMPANY (COPIES OF WHICH MAY BE OBTAINED FROM
     THE COMPANY).

                      REDEEMABLE WARRANT TO PURCHASE SHARES
                        OF COMMON STOCK OF CARDIMA, INC.

     This certifies that _________________ (the "Holder"), for value received is
entitled to purchase from Cardima, Inc., a Delaware corporation (the "Company"),
________________ (________) fully paid and nonassessable shares of the Company's
Common Stock (the "Warrant Shares") at a price of $[____][which shall be 150% of
the Purchase Price] per share (the "Stock Purchase Price") at any time or from
time to time on or after the Commencement Date (as defined below) up to and
including 5:00 p.m. (Pacific time) on the Expiration Date (as defined below),
upon surrender to the Company at its principal office at 47266 Benicia Street,
Fremont, California 94538 (or at such other location as the Company may advise
Holder in writing) of this Warrant properly endorsed with the Form of
Subscription attached hereto duly filled in and signed and upon payment by cash,
cashier's check or wire transfer of immediately available funds of the aggregate
Stock Purchase Price for the number of shares for which this Warrant is being
exercised determined in accordance with the provisions hereof, such exercise to
be conditioned upon the accuracy of all representations and warranties contained
in such Form of Subscription.  The Stock Purchase Price and the number of shares
purchasable hereunder are subject to adjustment as provided in Section 3 of this
Warrant.  "Commencement Date" means the date which is six (6) months after the
date of issuance of this Warrant and "Expiration Date" means the earlier of (i)
four (4) years from the date hereof, (ii) the occurrence of an event, proposal
of which is described in subsection (d) of Section 3.4 which causes termination
of this Warrant under Section 3.4, or (iii) on the date specified in the Notice
of Redemption (as defined below) pursuant to Section 7.  This Warrant is issued
pursuant to the Stock and Warrant Purchase Agreement between the Company and
Holder dated as of the date hereof (the "Purchase Agreement").

                                 Exhibit 1.1-1
<PAGE>

     This Warrant is subject to the following terms and conditions:

     1.  Exercise of Warrant
         -------------------

          1.1  Issuance of Certificates.  This Warrant is exercisable at the
               ------------------------
option of Holder at any time or from time to time on or after the Commencement
Date and prior to or on the Expiration Date for all or a portion of the shares
of Warrant Shares which may be purchased hereunder but if this Warrant is to be
exercised only in part, not for less than the greater of (a) twenty-five (25%)
of the number of Warrant Shares which may initially be purchased hereunder or
(b) one thousand (1,000) Warrant Shares (in either case as adjusted for any
stock dividend, split, combination, recapitalization or the like with respect to
such shares).  The Company agrees that the Warrant Shares purchased under this
Warrant shall be and are deemed to be issued to Holder as the record owner of
such shares as of the close of business on the date on which this Warrant shall
have been surrendered and payment made for such shares.  Subject to the
provisions of Section 2, certificates for the Warrant Shares so purchased,
together with any other securities or property to which Holder is entitled upon
such exercise, shall be delivered to Holder by the Company's transfer agent at
the Company's expense within a reasonable time after this Warrant has been
exercised.  Each stock certificate so delivered shall be in such denominations
of Warrant Shares as may be requested by Holder and shall be registered in the
name of Holder or such other name as shall be designated by Holder, subject to
the limitations contained in Section 2.  If, upon exercise of this Warrant,
fewer than all of the Warrant Shares evidenced by this Warrant are purchased
prior to the date of expiration of this Warrant, one or more new warrants
substantially in the form of, and on the terms in, this Warrant will be issued
for the remaining number of Warrant Shares not purchased upon exercise of this
Warrant.

          1.2  Payment.  Payment of the Stock Purchase Price shall be made by
               -------
surrender to the Company of this Warrant properly endorsed with the Form of
Subscription attached hereto duly filled in and signed and payment by cash,
cashier's check or wire transfer of immediately available funds and specifying
the number of Warrant Shares to be purchased, during normal business hours on
any day that is not a Saturday or Sunday or a day on which banks are required or
permitted to be closed in the State of California.

     2.  Shares to be Fully Paid; Reservation of Shares.  The Company covenants
         ----------------------------------------------
and agrees that all Warrant Shares which may be issued upon the exercise of the
rights represented by this Warrant will, upon issuance, be duly authorized,
validly issued, fully paid and nonassessable and free from all preemptive rights
of any stockholder and free of all taxes, liens and charges with respect to the
issue thereof.  The Company further covenants and agrees that during the period
within which the rights represented by this Warrant may be exercised, the
Company will use its best efforts to at all times have authorized and reserved,
for the purpose of issue or transfer upon exercise of this Warrant, a sufficient
number of shares of authorized but unissued Common Stock.  When and as required
to provide for the exercise of the rights represented by this Warrant, the
Company will take all such action as may be necessary to assure that such shares
of Common Stock may be issued as provided herein without violation of any
applicable law or regulation, or of any requirements of any domestic securities
exchange or automated quotation system upon which the Common Stock may be
listed.

     3.  Adjustment of Stock Purchase Price; Number of Shares.  The Stock
         ----------------------------------------------------
Purchase Price and the number of shares of Warrant Shares purchasable upon the
exercise of this Warrant shall be subject to adjustment from time to time upon
the occurrence of certain events described in this Section 3.

          3.1  Adjustment of Purchase Price.  In the event that the Company at
               ----------------------------
any time or from time to time after the issuance of this Warrant shall declare
or pay, without consideration, any dividend on the Common Stock payable in
Common Stock or in any right to acquire Common Stock for no consideration, or
shall effect a subdivision of the outstanding shares of Common Stock into a
greater number of shares of Common Stock (by stock split, reclassification or
otherwise than by payment of a dividend in Common Stock or in any right to
acquire Common Stock), or in the event the outstanding shares of Common Stock
shall be

                                 Exhibit 1.1-2
<PAGE>

combined or consolidated, by reclassification or otherwise, into a lesser number
of shares of Common Stock, then the Stock Purchase Price in effect immediately
prior to such event shall, concurrently with the effectiveness of such event, be
proportionately decreased or increased, as appropriate. In the event that the
Company shall declare or pay, without consideration, any dividend on the Common
Stock payable in any right to acquire Common Stock for no consideration, then
the Company shall be deemed to have made a dividend payable in Common Stock in
an amount of shares equal to the maximum number of shares issuable upon exercise
of such rights to acquire Common Stock. Upon each adjustment of the Stock
Purchase Price pursuant to this Section 3.1, the holder of this Warrant shall
thereafter be entitled to purchase, at the Stock Purchase Price resulting from
such adjustment, the number of shares of Common Stock obtained by multiplying
the Stock Purchase Price in effect immediately prior to such adjustment by the
number of shares of Common Stock purchasable pursuant hereto immediately prior
to such adjustment, and dividing the product thereof by the Stock Purchase Price
resulting from such adjustment.

          3.2  Adjustments for Reclassification and Reorganization.  If the
               ---------------------------------------------------
Common Stock shall be changed into the same or a different number of shares of
any other class or classes of stock, whether by capital reorganization,
reclassification or otherwise (other than a subdivision or combination of shares
provided for in Section 3.1), the Stock Purchase Price then in effect shall,
concurrently with the effectiveness of such reorganization or reclassification,
be proportionately adjusted so that this Warrant shall represent the right to
purchase, in lieu of the number of shares of Common Stock which this Warrant
would otherwise represent the right to purchase, a number of shares of such
other class or classes of stock equivalent to the number of shares of Common
Stock which this Warrant would have otherwise entitled the holder to purchase
immediately before that change.

          3.3  Notice of Adjustment.  Upon any adjustment of the Stock Purchase
               --------------------
Price or any increase or decrease in the number of shares of Common Stock
purchasable upon the exercise of this Warrant, the Company shall within five
business days give written notice thereof, by first class mail, postage prepaid,
(or by international delivery service, for international addresses) addressed to
the registered holder of this Warrant at the address of such holder as shown on
the books of the Company.  The notice shall be signed by the Company's chief
financial officer and shall state the Stock Purchase Price resulting from such
adjustment and the increase or decrease, if any, in the number of shares
purchasable at such price upon the exercise of this Warrant, setting forth in
reasonable detail the method of calculation and the facts upon which such
calculation is based.

          3.4  Certain Termination Events; Other Notices.  If at any time the
               -----------------------------------------
Company shall propose to:

               (a) declare any cash dividend upon its Common Stock;

               (b) declare or make any dividend or other distribution to the
holders of its Common Stock, whether in cash, property or other securities;

               (c) effect any reorganization or reclassification of the capital
stock of the Company or any consolidation or merger of the Company with or into
another corporation or any sale, lease or conveyance of all or substantially all
of the property of the Company; or

               (d) effect a voluntary or involuntary dissolution, liquidation or
winding-up of the Company;

then, in any one or more of said cases, the Company shall give, by certified or
registered mail, postage prepaid, or international delivery service for
international deliveries, addressed to the holder of this Warrant at the address
of such holder as shown on the books of the Company, (i) at least fifteen (15)
business days' prior written notice of the date on which the books of the
Company shall close or a record shall be taken for such

                                 Exhibit 1.1-3
<PAGE>

dividend or distribution or for determining rights to vote in respect of any
such reorganization, reclassification, consolidation, merger, sale, lease,
conveyance, dissolution, liquidation or winding-up, and (ii) in the case of any
such reorganization, reclassification, consolidation, merger, sale, lease,
conveyance, dissolution, liquidation or winding-up, at least fifteen (15)
business days' written notice of the date when the same shall take place. Any
notice given in accordance with clause (i) above shall also specify, in the case
of any such dividend or distribution, the record date for such dividend or
distribution, if after the Commencement Date. Any notice given in accordance
with clause (ii) above shall also specify the date on which the holders of
Common Stock shall be entitled to exchange their Common Stock for securities or
other property, if any, deliverable upon such reorganization, reclassification,
consolidation/merger, sale, lease, conveyance, dissolution, liquidation or
winding-up, as the case may be and in connection with the occurrence of an event
described in clause (d) above such notice shall specify the anticipated net
equity value that will accrue to Common Stock holders so that the Holder can
make an informed decision whether or not to exercise this Warrant. In the event
that the Holder of the Warrant does not exercise this Warrant prior to the
occurrence of an event described in clause (a) or (b) above, the Holder shall
not be entitled to receive the benefits accruing to existing holders of the
Common Stock in such event. Upon the occurrence of an event described in clause
(c) in which the holders of the Company's voting securities of the Company
immediately prior to the event do not hold at least fifty percent (50%) of the
voting securities of the Company or the surviving entity (in a sale of assets,
the Company shall be the surviving entity) resulting from such event immediately
after such event, this Warrant shall terminate unless the Company has negotiated
(which it is under no obligation to do) for the assumption of this Warrant. Upon
the occurrence of an event described in clause (c) and, subject to the
immediately preceding sentence, the Holder shall be entitled thereafter, upon
payment of the Stock Purchase Price in effect immediately prior to such action,
to receive upon exercise of this Warrant the class and number of shares which
the Holder would have been entitled to receive after the occurrence of such
event had this Warrant been exercised immediately prior to such event. In
connection with the transactions described in clause (c) and provided that this
Warrant does not terminate as provided in the second sentence immediately
preceding this sentence, the Company will require each person (other than the
Company) that may be required to deliver any cash, stock, securities or other
property upon the exercise of this Warrant as provided herein to assume, by
written instrument delivered to the Holder of this Warrant (x) the obligations
of the Company under this Warrant and (y) the obligation to deliver to such
Holder such cash, stock, securities or other property as such Holder may be
entitled to receive in accordance with the provisions of this Section 3. Upon
the occurrence of an event the proposal of which is described in clause (d),
this Warrant shall terminate. Notwithstanding any other provision hereof, no
Holder shall have the right to obtain an injunction or restraining order or
otherwise interfere with or prevent the occurrence of any of the actions
described in (a) - (d) above.

          3.5  Adjustment of Number of Warrant Shares.  The number of Warrant
               --------------------------------------
Shares purchasable hereunder shall be reduced on a one-for-one basis by the
number of shares of Common Stock (or Common Stock equivalents) sold directly or
indirectly, including, without limitation, any short sale, third party short
sales or holdings of a "put equivalent position" (as defined in Rule 16a-1 of
the 1934 Act), of the Company's Common Stock by the Holder from the date hereof
until the Commencement Date.  Prior to or simultaneously with the first exercise
of this Warrant by the Holder (or the transfer of this Warrant), the Holder
shall provide the Company with an affidavit and other reasonable supporting
materials as to the foregoing.

     4.  Issue Tax.  The issuance of certificates for the Warrant Shares upon
         ---------
the exercise of the Warrant shall be made without charge to the Holder of the
Warrant for any issue tax in respect thereof; provided, however, that the
                                              --------  -------
Company shall not be required to pay any tax which may be payable in respect of
any transfer involved in the issuance and delivery of any certificate in a name
other than that of the then Holder of the Warrant being exercised.

     5.  No Voting or Dividend Rights; Limitation of Liability.  Nothing
         -----------------------------------------------------
contained in this Warrant shall be construed as conferring upon the Holder
hereof the right to vote or to consent or to receive notice as

                                 Exhibit 1.1-4
<PAGE>

a stockholder in respect of meetings of stockholders for the election of
directors of the Company or any other matters or any rights whatsoever as a
stockholder of the Company. Except for the adjustment to the Stock Purchase
Price pursuant to Section 3.1 in the event of a dividend on the Common Stock
payable in shares of Common Stock, no dividends or interest shall be payable or
accrued in respect of this Warrant or the interest represented hereby or the
shares purchasable hereunder until, and only to the extent that, this Warrant
shall have been exercised. No provisions hereof, in the absence of affirmative
action by the Holder to purchase shares of Warrant Shares, and no mere
enumeration herein of the rights or privileges of the Holder hereof, shall give
rise to any liability of such Holder for the Stock Purchase Price or as a
stockholder of the Company whether such liability is asserted by the Company or
by its creditors.

     6.  Restrictions on Transferability of Securities: Compliance With
         --------------------------------------------------------------
Securities Act.
--------------

          6.1  Restrictions on Transferability.  The Warrant and the Warrant
               -------------------------------
Shares (collectively, the "Securities") shall not be transferable except upon
the conditions specified in the Purchase Agreement, which conditions are
intended to insure compliance with the provisions of the Securities Act and
applicable "blue sky" law.

          6.2  Restrictive Legend.  Each certificate representing the Securities
               ------------------
or any other securities issued in respect of the Securities upon any stock
split, stock dividend, recapitalization, merger, consolidation or similar event,
shall (unless otherwise permitted by the provisions of the Purchase Agreement)
be stamped or otherwise imprinted with a legend substantially in the following
form (in addition to any legend required under applicable state securities
laws):

          THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE BEEN ACQUIRED FOR
          INVESTMENT AND HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF
          1933, AS AMENDED (THE "SECURITIES ACT").  THE SECURITIES MAY NOT BE
          SOLD, TRANSFERRED, ASSIGNED OR HYPOTHECATED UNLESS REGISTERED UNDER
          THE SECURITIES ACT AND QUALIFIED UNDER APPLICABLE STATE SECURITIES
          LAWS OR UNLESS SUCH SALE, TRANSFER, ASSIGNMENT OR HYPOTHECATION IS
          EXEMPT FROM THE REGISTRATION REQUIREMENTS OF THE SECURITIES ACT AND
          THE QUALIFICATION REQUIREMENTS OF APPLICABLE STATE SECURITIES LAWS AND
          THE COMPANY RECEIVES AN OPINION OF COUNSEL SATISFACTORY TO THE COMPANY
          THAT SUCH REGISTRATION AND QUALIFICATION ARE NOT REQUIRED.  THE
          SECURITIES REPRESENTED BY THIS CERTIFICATE AND THE RIGHTS OF HOLDERS
          THEREOF ARE SUBJECT TO CERTAIN RESTRICTIONS ON TRANSFER AND OTHER
          RESTRICTIONS, AND THE HOLDER OF THE SECURITIES REPRESENTED BY THIS
          CERTIFICATE (INCLUDING ANY FUTURE HOLDERS) IS BOUND BY THE TERMS OF A
          STOCK AND WARRANT PURCHASE AGREEMENT BETWEEN THE ORIGINAL PURCHASER
          AND THE COMPANY (COPIES OF WHICH MAY BE OBTAINED FROM THE COMPANY).

          6.3  Exchange of Warrant.  Subject to the terms and conditions hereof,
               -------------------
including the restrictions on transfer in this Section 6 and in the Purchase
Agreement, upon surrender of this Warrant to the Company with a duly executed
Assignment Form in the form attached hereto and funds sufficient to pay any
transfer tax, the Company shall, without charge, execute and deliver a new
Warrant or Warrants of like tenor in the name of the assignee named in such
Assignment Form and this Warrant shall promptly be canceled; provided, however,
                                                             --------  -------
that if the transfer is for less than all of this Warrant, the transferor shall
pay all reasonable costs of the Company in connection with a transfer of
Warrants to purchase less than the greater of (a) twenty-five percent (25%) of
the Warrant Shares which may initially be purchased hereunder or (b) one
thousand (1,000) Warrant Shares (in either case as adjusted for any stock
dividend, split, combination,

                                 Exhibit 1.1-5
<PAGE>

recapitalization or the like with respect to such shares). The term "Warrant" as
used herein shall be deemed to include any Warrants issued in exchange for this
Warrant.

          6.4  Ownership of Warrant.  The Company may deem and treat the person
               --------------------
in whose name this Warrant is registered as the holder and owner hereof
(notwithstanding any notations of ownership or writing hereon made by anyone
other than the Company) for all purposes and shall not be affected by any notice
to the contrary, until presentation of this Warrant for registration of transfer
as provided in Section 6.3.

     7.  Redemption.  This Warrant may be redeemed at the option of the Company
         ----------
at a redemption price of $0.001 per Warrant Share (subject to adjustment in good
faith by the Company's Board of Directors in the event of stock splits or other
events described in Section 3.1 or 3.2 above) (the "Redemption Price"), at any
time after the date hereof provided that (i) the average closing bid price of
the Common Stock as reported by the National Association of Securities Dealers
Automated Quotation ("NASDAQ") or the OTC Bulletin Board, shall have been $____[
which shall be 200% of the Purchase Price] for fifteen (15) consecutive trading
days (the "Triggering Event") during a period ending within five (5) business
days prior to the Redemption Notice Date (as defined below) (subject to
adjustment in good faith by the Company's Board of Directors in the event of any
stock splits or other events described in Section 3.1 or 3.2 above); provided,
                                                                     --------
that at any time after the Redemption Notice Date (as defined below) and prior
to the Redemption Date (as defined below) the Holder may exercise this Warrant,
provided, further, in the event that the Redemption Notice Date is prior to the
six (6) months after the date hereof, the Commencement Date shall be deemed to
be the Redemption Notice Date, and notwithstanding anything herein or in the
Purchase Agreement to the contrary, after such date the Holder may exercise this
Warrant at any time prior to the Redemption Date.  The Company shall provide
written notice of redemption which shall specify the Redemption Date (the
"Notice of Redemption") to the Holder not later than five (5) business days
after the Triggering Event.  On or after the date fixed for redemption (the
"Redemption Date") which shall be no less than thirty (30) days after the date
that the Notice of Redemption is sent to the Holder (the "Redemption Notice
Date"), the Holder shall have no rights with respect to this Warrant except to
receive the Redemption Price upon surrender of this Warrant Certificate.

     8.  Modification and Waiver.  Except as otherwise provided herein, this
         -----------------------
Warrant and any provision hereof may be changed, waived, discharged or
terminated only by an instrument in writing signed by the party against which
enforcement of the same is sought.

     9.  Notices.  Except as otherwise provided herein, any notice, request or
         -------
other document required or permitted to be given or delivered to the holder
hereof or the Company shall be delivered or shall be sent by United States
certified or registered mail, postage prepaid, (or international delivery
service for international deliveries) to Holder at its address as shown on the
books of the Company or to the Company at the address indicated therefor in the
first paragraph of this Warrant.

     10.  Descriptive Headings and Governing Law.  The descriptive headings of
          --------------------------------------
the several sections and paragraphs of this Warrant are inserted for convenience
only and do not constitute a part of this Warrant.  This Warrant shall be
construed and enforced in accordance with, and the rights of the parties shall
be governed by, the laws of the State of California (without regard to its
conflicts of law provisions).  The Holder hereby irrevocably submits to the
jurisdiction of any State or United States Federal court sitting in the Alameda
or San Francisco counties in the State of California over any action or
proceeding arising out of or relating to this Warrant or any agreement
contemplated hereby, and the Holder irrevocably agrees that all claims in
respect of such action or proceeding may be heard and determined in such State
or Federal court.  The Holder further waives any objection to venue in such
State and any objection to an action or proceeding in such State based on non-
convenient forum.  The Holder further agrees that any action or proceeding
brought against the Company shall be brought only in the State or United States
Federal courts sitting in Alameda or San Francisco counties in the State of
California.  THE HOLDER AGREES TO WAIVE ITS

                                 Exhibit 1.1-6
<PAGE>

RIGHTS TO A JURY TRIAL OR ANY CLAIM FOR CAUSE OF ACTION BASED UPON OR ARISING
OUT OF THIS WARRANT OR ANY DOCUMENT OR AGREEMENT CONTEMPLATED HEREBY.

     11.  Lost Warrants or Stock Certificates.  The Company represents and
          -----------------------------------
warrants to Holder that upon receipt of evidence reasonably satisfactory to the
Company of the loss, theft, destruction, or mutilation of any Warrant or stock
certificate and, in the case of any such loss, theft or destruction, upon
receipt of an indemnity and, if requested, bond reasonably satisfactory to the
Company, or, in the case of any such mutilation, upon surrender and cancellation
of such Warrant or stock certificate, the Company at its expense will make and
deliver a new Warrant or stock certificate, of like tenor, in lieu of the lost,
stolen, destroyed or mutilated Warrant or stock certificate.

     12.  Amendment.  This Warrant is one of a series of warrants (the "Warrant
          ---------
Series") to purchase in the aggregate up to seven million five hundred thousand
(7,500,000) shares of the Company's Common Stock.  This Warrant may be amended
only with the written approval of the Company and (i) the Holder of this Warrant
or (ii) the holders of a majority of the warrants in the Warrant Series;

provided, however, that any amendment affected pursuant to (ii) above shall be
--------  -------
made in the same manner to all warrants in the Warrant Series.

     13.  Binding Effect; Benefits.  This Warrant shall inure to the benefit of
          ------------------------
and shall be binding upon the Company and the Holder and their respective heirs,
legal representatives, successors and assigns.  Nothing in this Warrant,
expressed or implied, is intended to or shall confer on any person other than
the Company and the Holder, or their respective heirs, legal representatives,
successors or assigns, any rights, remedies, obligations or liabilities under or
by reason of this Warrant.

     14.  Fractional Shares.  No fractional shares shall be issued upon exercise
          -----------------
of this Warrant.  The Company shall, in lieu of issuing any fractional share,
pay the Holder entitled to such fraction a sum in cash equal to such fraction
multiplied by the market price of the Common Stock on such exercise date, which
shall be, on such date, the closing price for the Common Stock or the closing
bid if no sales were reported, as quoted on the exchange or market that is the
primary trading market for the Company.

     IN WITNESS WHEREOF, the Company has caused this Warrant to be executed by
its officers, thereunto duly authorized this ____ day of May, 2001.

                              CARDIMA, INC., a Delaware corporation

                              By:
                                  _____________________________________
                                    Name:
                                    Title:

                                 Exhibit 1.1-7
<PAGE>

                              FORM OF SUBSCRIPTION
                              --------------------

                  (To be signed only upon exercise of Warrant)

To:  Cardima, Inc.

     The undersigned, the holder of the within Warrant, hereby irrevocably
elects to exercise such Warrant for, and to purchase thereunder,
________________ (________) shares of Common Stock of Cardima, Inc. (the
"Company"), and herewith makes payment in the amount of $________ therefor.  The
certificates for such shares should be issued in the name of, and delivered to,
________________ whose address is
__________________________________________________

__________________________________________________________.

     The undersigned represents, unless the exercise of this Warrant has been
registered under the Securities Act of 1933, as amended (the "Securities Act"),
that (i) the undersigned is acquiring such Common Stock for his or its own
account for investment and not with a view to or for sale in connection with any
distribution thereof (except for any resale pursuant to a registration statement
under the Securities Act), (ii) the undersigned has such knowledge and
experience in financial and business matters as to be capable of evaluating the
merits and risks of the undersigned's investment in the shares of Common Stock,
(iii) the undersigned has received all of the information the undersigned
requested from the Company and the undersigned considers necessary or
appropriate for deciding whether to purchase the shares, (iv) the undersigned
has the ability to bear the economic risks of the undersigned's prospective
investment and (v) the undersigned is able, without materially impairing his
financial condition, to hold the shares of Common Stock for an indefinite period
of time and to suffer complete loss on the undersigned's investment.

     The undersigned is an "accredited investor" as defined in Regulation D of
the Securities and Exchange Commission on the date hereof.

DATED:
       ______________________
                                _______________________________________
                               (Signature must conform in all respects to name
                               of holder as specified on the face of the
                               Warrant)

                                _______________________________________

                                _______________________________________
                               (Address)

                                 Exhibit 1.1-8
<PAGE>

THIS WARRANT AND ANY SHARES ACQUIRED UPON THE EXERCISE OF THIS WARRANT HAVE NOT
BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, AND MAY NOT BE
SOLD OR OTHERWISE TRANSFERRED EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION
STATEMENT FILED UNDER SUCH ACT OR PURSUANT TO AN EXEMPTION FROM REGISTRATION
UNDER SUCH ACT.

                                ASSIGNMENT FORM
                                ---------------

              (To be executed only upon transfer of this Warrant)

     For value received, the undersigned registered holder of the within Warrant
hereby sells, assigns and transfers unto ____________________ (the "Assignee")
the right represented by such Warrant to purchase __________ Warrant Shares and
all other rights of the Holder with respect thereto under the within Warrant,
and appoints _________________ as Attorney to make such transfer on the books of
Cardima, Inc. maintained for such purpose, with full power of substitution in
the premises.

     The undersigned also represents that, by assignment hereof, the Assignee
acknowledges that this Warrant and the Warrant Shares to be issued upon exercise
hereof are being acquired for investment and that the Assignee will not offer,
sell or otherwise dispose of this Warrant or any Warrant Shares to be issued
upon exercise hereof except under circumstances that will not result in a
violation of the Securities Act of 1933, as amended, or any state securities
laws.  Further, the Assignee has acknowledged that upon exercise of this
Warrant, the Assignee shall, if requested by the Company, confirm in writing, in
a form satisfactory to the Company, that the Warrant Shares so purchased are
being acquired for investment and not with a view toward distribution or resale.

Dated:  ____________________.

                                  _____________________________________________
                                  (Signature)

                                  _____________________________________________
                                  (Print Name)

                                  _____________________________________________
                                  (Street Address)

                                  _____________________________________________
                                  (City)                  (State)     (Zip Code)

                                 Exhibit 1.1-9
<PAGE>

                                                                     Exhibit 2.1
                                                                     -----------

                                    DOMESTIC
                               WIRE INSTRUCTIONS

BANK:                         SILICON VALLEY BANK
                              3003 TASMAN DRIVE
                              SANTA CLARA, CA
95054

ABA ROUTING & TRANSIT:        121140399

FOR CREDIT OF:                CARDIMA

CREDIT ACCOUNT #:             0272686670

BY ORDER OF:                  {NAME OF SENDER}

                                  Exhibit 2.1
<PAGE>

                                                                     Exhibit 4.9
                                                                     -----------

                      INVESTMENT REPRESENTATION STATEMENT

     1.  Acquisition Entirely for Own Account.  Purchaser represents and
         ------------------------------------
warrants that Purchaser is acquiring the Securities solely for Purchaser's own
account for investment and not with a view to sale or distribution of the
Securities or any portion or component thereof, and Purchaser will not sell,
offer to sell or otherwise dispose of or distribute the Securities or any
portion or component thereof in any transaction other than a transaction
complying with the registration requirements of the Securities Act, and
applicable state securities or "Blue Sky" laws, or pursuant to an exemption
therefrom.  Purchaser also represents that the entire legal and beneficial
interest of the Securities that Purchaser is acquiring is being acquired for,
and will be held for Purchaser's account only, and neither in whole nor in part
for any other person or entity.

     2.  Information Concerning the Company.  Purchaser represents and warrants
         ----------------------------------
that Purchaser has been provided with such information concerning the Company
that Purchaser deems necessary and appropriate to enable Purchaser to evaluate
the financial risk inherent in making an investment in the Securities.
Purchaser further acknowledges that Purchaser has received satisfactory and
complete information concerning the business and financial condition of the
Company in response to all inquiries in respect thereof.

     3.  Economic Risk and Suitability.  Purchaser represents and warrants as
         -----------------------------
follows:

          3.1  Purchaser acknowledges and realizes that Purchaser's purchase of
the Securities involves a high degree of risk and will be a highly speculative
investment and that Purchaser is able, without impairing Purchaser's financial
condition, to hold the Securities for an indefinite period of time and to suffer
a complete loss of Purchaser's investment.

          3.2  Purchaser has carefully considered and has, to the extent
Purchaser believes such discussions necessary, discussed with Purchaser's
professional, legal, tax and financial advisors the suitability of an investment
in the Securities for the particular legal, tax and financial situation of
Purchaser and that Purchaser and/or Purchaser's advisors have determined that
the Securities are a suitable investment for Purchaser.

          3.3  Purchaser has such knowledge and experience in business and
financial matters, including without limitation, investment in technology and
biotechnology companies, as will enable Purchaser to fend for itself, bear the
economic risks of its investment and evaluate the merits and risks of an
investment in the Securities and to make an informed investment decision.

          3.4  Purchaser has carefully read the Purchase Agreement and all
attachments thereto and the Company has made available to Purchaser or
Purchaser's advisors all information and documents requested by Purchaser
relating to investment in the Securities, and has provided answers to
Purchaser's satisfaction to all of Purchaser's questions concerning the Company
and the Securities to be acquired.

          3.5  Purchaser understands that neither the Company nor any of its
officers/directors, has any obligation to register the Securities under any
federal or state securities act or law except as otherwise expressly set forth
in Section 5.3 of the Annex to the Purchase Agreement.

          3.6  All information that Purchaser has provided concerning himself or
herself, his or her financial position and (each of) his/her representative(s),
if any, is correct and complete as of the date set forth below, and if there
should be any material change in such information, Purchaser will provide such
information to the Company as soon as practicable thereafter.

                                 Exhibit 4.9-1
<PAGE>

          3.7  Purchaser understands that the Company is relying on the truth
and accuracy of the declarations, representations, warranties and agreements
made by Purchaser to the Company herein in transferring the Securities to
Purchaser.

          3.8  Purchaser confirms that Purchaser has received no general
solicitation or general advertisement and has attended no seminar or meeting
(whose attendees have been invited by any general solicitation or general
advertisement) and has received no advertisement, article, notice or other
communication published in any newspaper, magazine, or similar media or
broadcast or television or radio regarding the Offering of the Securities.

     4.  Status of Purchaser.  Purchaser represents and warrants that Purchaser
         -------------------
is an "Accredited Investor", as defined in Rule 501 of the SEC, because
Purchaser is either (Please check all item(s) that apply):

     [_]  (a)  A natural person whose individual net worth, or joint net worth
               with that person's spouse, at the time of his/her purchase,
               exceeds $1 million; or

     [_]  (b)  A natural person who had individual income in excess of $200,000
               in each of the two most recent years or joint income with that
               person's spouse in excess of $300,000 in each of those years and
               has a reasonable expectation of reaching the same income level in
               the current year;

     [_]  (c)  a bank as defined in Section 3(a)(2) of the Securities Act;

     [_]  (d)  a savings and loan association or other institution as defined in
               Section 3(a)(5)(A) of the Securities Act, whether acting in its
               individual or fiduciary capacity;

     [_]  (e)  a broker dealer registered pursuant to Section 15 of the Exchange
               Act;

     [_]  (f)  an insurance company as defined in Section 2(13) of the
               Securities Act;

     [_]  (g)  an investment company registered under the Investment Company Act
               of 1940, as amended, or a business development company as defined
               in Section 2(a)(48) of the Securities Act;

     [_]  (h)  a small business investment company licensed under the U.S. Small
               Business Administration under Section 301(c) or (d) of the Small
               Business Investment Act of 1958;

     [_]  (i)  a private business development company as defined in Section
               202(a)(22) of the Investment Advisers Act of 1940, as amended;

     [_]  (j)  a corporation, partnership, an organization described in Section
               501)(3) of the Internal Revenue Code of 1986, or a Massachusetts
               or similar business trust, not formed for the specific purpose of
               acquiring the Securities, with total assets in excess of
               $5,000,000;

     [_]  (k)  a trust, with total assets in excess of $5,000,000 not formed for
               the specific purpose of acquiring the Securities, whose purchase
               of the Securities is directed by a sophisticated person as
               described in Rule 506(b)(ii) of Regulation D promulgated under
               the Securities Act; or

                                 Exhibit 4.9-2
<PAGE>

     [_]  (l)  an entity in which all of the equity owners meet one of the
               requirements of paragraphs (a) through (k) hereof.

     5.  Residency.  The undersigned is a bona fide resident of ______________.
         ---------

     Dated:
            ___________________         ________________________________________
                                                       (signature)

                                        _______________________________________
                                                       (print name)

                                 Exhibit 4.9-3<PAGE>

                                                                    EXHIBIT 10.2

Warrant No. _______________

     THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE BEEN ACQUIRED FOR
     INVESTMENT AND HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933,
     AS AMENDED (THE "SECURITIES ACT").  THE SECURITIES MAY NOT BE SOLD,
     TRANSFERRED, ASSIGNED OR HYPOTHECATED UNLESS REGISTERED UNDER THE
     SECURITIES ACT AND QUALIFIED UNDER APPLICABLE STATE SECURITIES LAWS OR
     UNLESS SUCH SALE, TRANSFER, ASSIGNMENT OR HYPOTHECATION IS EXEMPT FROM THE
     REGISTRATION REQUIREMENTS OF THE SECURITIES ACT AND THE QUALIFICATION
     REQUIREMENTS OF APPLICABLE STATE SECURITIES LAWS AND THE COMPANY RECEIVES
     AN OPINION OF COUNSEL SATISFACTORY TO THE COMPANY THAT SUCH REGISTRATION
     AND QUALIFICATION ARE NOT REQUIRED.  THE SECURITIES REPRESENTED BY THIS
     CERTIFICATE AND THE RIGHTS OF HOLDERS THEREOF ARE SUBJECT TO CERTAIN
     RESTRICTIONS ON TRANSFER AND OTHER RESTRICTIONS.

                           WARRANT TO PURCHASE SHARES
                        OF COMMON STOCK OF CARDIMA, INC.

     This certifies that, for value received, _________________ (the "Holder"),
is entitled, subject to the terms and conditions set forth below, to purchase
from Cardima, Inc., a Delaware corporation (the "Company") in whole or in part,
________________ (________) fully paid and nonassessable shares of the Company's
Common Stock, par value $0.001 per share (the "Warrant Shares") at a price of
$0.638 per share (the "Stock Purchase Price") at any time or from time to time
up to and including 5:00 p.m. (Pacific time) on the Expiration Date (as defined
below), upon surrender to the Company at its principal office at 47266 Benicia
Street, Fremont, California 94538 (or at such other location as the Company may
advise Holder in writing) of this Warrant properly endorsed with the Form of
Subscription attached hereto duly filled in and signed and upon payment by cash,
cashier's check or wire transfer of immediately available funds of the aggregate
Stock Purchase Price for the number of shares for which this Warrant is being
exercised determined in accordance with the provisions hereof or otherwise as
hereinafter provided, such exercise to be conditioned upon the accuracy of all
representations and warranties contained in Section __ hereof.  The Stock
Purchase Price and the number of shares purchasable hereunder are subject to
adjustment as provided in Section 3 of this Warrant.  "Expiration Date" means
May 3, 2006.  This Warrant is issued pursuant to the Engagement Letter Agreement
between the Company and Holder dated as of April 10, 2001 (the "Agreement").

     1.  Exercise of Warrant
         -------------------

         1.1  Issuance of Certificates.  This Warrant is exercisable at the
              ------------------------
option of Holder at any time or from time to time prior to or on the Expiration
Date for all or a portion of the shares of Warrant Shares which may be purchased
hereunder but if this Warrant is to be exercised only in part, not for less than
(i) twenty-five thousand (25,000) Warrant Shares or (ii) such lesser number of
shares which may then constitute the maximum number purchasable (in either case
as adjusted for any stock dividend, split, combination, recapitalization or the
like with respect to such shares).  The Company agrees that the Warrant Shares
purchased under this Warrant shall be and are deemed to be issued to Holder as
the record owner of such shares as of the close of business on the date on which
this Warrant shall have been surrendered and payment made for such shares.
Subject to the provisions of Section 2, certificates for the Warrant Shares so
purchased, together with any other securities or property to which Holder is
entitled upon such exercise, shall be delivered to Holder by the Company's
transfer agent at the Company's expense within a reasonable time
<PAGE>

after this Warrant has been exercised. Each stock certificate so delivered shall
be in such denominations of Warrant Shares as may be requested by Holder and
shall be registered in the name of Holder or such other name as shall be
designated by Holder, subject to the limitations contained in Section 2. If,
upon exercise of this Warrant, fewer than all of the Warrant Shares evidenced by
this Warrant are purchased prior to the date of expiration of this Warrant, one
or more new warrants substantially in the form of, and on the terms in, this
Warrant will be issued for the remaining number of Warrant Shares not purchased
upon exercise of this Warrant.

         1.2  Payment.  Payment of the Stock Purchase Price shall be made at
              -------
the option of the Holder by surrender to the Company of this Warrant properly
endorsed with the Form of Subscription attached hereto duly filled in and signed
and (i) payment by cash, cashier's check or wire transfer of immediately
available funds or (ii) by surrender of this Warrant to the Company, with a duly
executed exercise notice marked to reflect "Net Issue Exercise," and in either
case specifying the number of Warrant Shares to be purchased, during normal
business hours on any day that is not a Saturday or Sunday or a day on which
banks are required or permitted to be closed in the State of California.

         1.3  Net Issue Exercise.  Upon a Net Issue Exercise, the Holder shall
              ------------------
be entitled to receive Warrant Shares equal to the value of this Warrant (or the
portion thereof being exercised by Net Issue Exercise) by surrender of this
Warrant to the Company together with notice of such election in which event, the
Company shall issue to Holder a number of Warrant Shares computed as of the date
of surrender of this Warrant to the Company using the following formula:

            X= Y(A-B)
               ------
                  A

    Where:  X=  the number of Warrant Shares to be issued to Holder under this
                Section 1.3;

            Y=  the number of Warrant Shares otherwise purchasable under this
                Warrant (as adjusted to the date of such calculation);

            A=  the fair market value of one share of the Common Stock (at the
                date of calculation);

            B=  the Stock Purchase Price (as adjusted to the date of such
                calculation).

     For purposes of this Section 1.3, the fair market value of the Company's
Common Stock shall mean (A) the average closing bid price of the Company's
Common Stock quoted on any exchange, including the Nasdaq SmallCap Market, on
which the Common Stock is listed, as published in the Western Edition of the The
Wall Street Journal for the five (5) consecutive trading days immediately prior
to the date the Holder delivers its notice of Net Issue Exercise to the Company
or (B) the average of the closing bid prices of the Company's Common Stock
quoted in the Over-The-Counter Market Summary, if applicable, for the five (5)
consecutive trading days immediately prior to the date the Holder delivers its
notice of Net Issue Exercise to the Company, or (C) if neither (A) nor (B) is
applicable, the price determined by the Company's Board of Directors, acting in
good faith upon a review of all relevant factors.

     2.  Shares to be Fully Paid; Reservation of Shares.  The Company covenants
         ----------------------------------------------
and agrees that all Warrant Shares which may be issued upon the exercise of the
rights represented by this Warrant will, upon issuance, be duly authorized,
validly issued, fully paid and nonassessable and free from all preemptive rights
of any stockholder and free of all taxes, liens and charges with respect to the
issue thereof.  The Company further covenants and agrees that during the period
within which the rights represented by this Warrant may be exercised, the
Company will use its best efforts to at all times have authorized and reserved,
for the purpose of issue or transfer upon exercise of this Warrant, a sufficient
number of shares of authorized but
<PAGE>

unissued Common Stock. When and as required to provide for the exercise of the
rights represented by this Warrant, the Company will take all such action as may
be necessary to assure that such shares of Common Stock may be issued as
provided herein without violation of any applicable law or regulation, or of any
requirements of any domestic securities exchange or automated quotation system
upon which the Common Stock may be listed.

     3.  Adjustment of Stock Purchase Price; Number of Shares.  The Stock
         ----------------------------------------------------
Purchase Price and the number of shares of Warrant Shares purchasable upon the
exercise of this Warrant shall be subject to adjustment from time to time upon
the occurrence of certain events described in this Section 3.

         3.1  Adjustment of Purchase Price.  In the event that the Company at
              ----------------------------
any time or from time to time after the issuance of this Warrant shall declare
or pay, without consideration, any dividend on the Common Stock payable in
Common Stock or in any right to acquire Common Stock for no consideration, or
shall effect a subdivision of the outstanding shares of Common Stock into a
greater number of shares of Common Stock (by stock split, reclassification or
otherwise than by payment of a dividend in Common Stock or in any right to
acquire Common Stock), or in the event the outstanding shares of Common Stock
shall be combined or consolidated, by reclassification or otherwise, into a
lesser number of shares of Common Stock, then the Stock Purchase Price in effect
immediately prior to such event shall, concurrently with the effectiveness of
such event, be proportionately decreased or increased, as appropriate.  In the
event that the Company shall declare or pay, without consideration, any dividend
on the Common Stock payable in any right to acquire Common Stock for no
consideration, then the Company shall be deemed to have made a dividend payable
in Common Stock in an amount of shares equal to the maximum number of shares
issuable upon exercise of such rights to acquire Common Stock.  Upon each
adjustment of the Stock Purchase Price pursuant to this Section 3.1, the holder
of this Warrant shall thereafter be entitled to purchase, at the Stock Purchase
Price resulting from such adjustment, the number of shares of Common Stock
obtained by multiplying the Stock Purchase Price in effect immediately prior to
such adjustment by the number of shares of Common Stock purchasable pursuant
hereto immediately prior to such adjustment, and dividing the product thereof by
the Stock Purchase Price resulting from such adjustment.

         3.2  Adjustments for Reclassification and Reorganization.  If the
              ---------------------------------------------------
Common Stock shall be changed into the same or a different number of shares of
any other class or classes of stock, whether by capital reorganization,
reclassification or otherwise (other than a subdivision or combination of shares
provided for in Section 3.1), the Stock Purchase Price then in effect shall,
concurrently with the effectiveness of such reorganization or reclassification,
be proportionately adjusted so that this Warrant shall represent the right to
purchase, in lieu of the number of shares of Common Stock which this Warrant
would otherwise represent the right to purchase, a number of shares of such
other class or classes of stock equivalent to the number of shares of Common
Stock which this Warrant would have otherwise entitled the holder to purchase
immediately before that change.

         3.3  Adjustments for Merger, Sale of Assets, Etc.  In the event that
              -------------------------------------------
the Company at any time while this Warrant, or any portion thereof, is
outstanding and unexpired, shall (i) merge or consolidate with or into another
corporation in which the Company is not the surviving entity (or enters into a
reverse triangular merger in which the Company is the surviving entity but that
the shares of common stock outstanding immediately prior to the merger are
converted by virtue of the merger into other property, whether in the form of
securities, cash or otherwise) or (ii) sell or transfer all or substantially of
all its assets, as part of such merger, consolidation, sale or transfer, lawful
provision shall be made so that the Holder shall hereafter be entitled to
receive upon exercise of this Warrant, during such period specified herein and
upon payment of the Stock Purchase Price then in effect, the number of shares of
stock or other securities or properties of the successor corporation resulting
from such transaction, which a holder of the shares deliverable upon exercise of
this Warrant would have been entitled to receive in such transaction if this
Warrant had been exercised immediately prior to such transaction, all subject to
further adjustment as provided in this Section 3.
<PAGE>

         3.4  Notice of Adjustment.  Upon any adjustment of the Stock Purchase
              --------------------
Price or any increase or decrease in the number of shares of Common Stock
purchasable upon the exercise of this Warrant, the Company shall within five
business days give written notice thereof, by first class mail, postage prepaid,
(or by international delivery service, for international addresses) addressed to
the registered holder of this Warrant at the address of such holder as shown on
the books of the Company.  The notice shall be signed by the Company's chief
financial officer and shall state the Stock Purchase Price resulting from such
adjustment and the increase or decrease, if any, in the number of shares
purchasable at such price upon the exercise of this Warrant, setting forth in
reasonable detail the method of calculation and the facts upon which such
calculation is based.

         3.5  Other Notices.  If at any time the Company shall propose to:
              -------------

              (a) declare any cash dividend upon its Common Stock;

              (b) declare or make any dividend or other distribution to the
holders of its Common Stock, whether in cash, property or other securities;

              (c) effect any reorganization or reclassification of the capital
stock of the Company or any consolidation or merger of the Company with or into
another corporation or any sale, lease or conveyance of all or substantially all
of the property of the Company; or

              (d) effect a voluntary or involuntary dissolution, liquidation or
winding-up of the Company;

then, in any one or more of said cases, the Company shall give, by certified or
registered mail, postage prepaid, or international delivery service for
international deliveries, addressed to the holder of this Warrant at the address
of such holder as shown on the books of the Company, (i) at least fifteen (15)
business days' prior written notice of the date on which the books of the
Company shall close or a record shall be taken for such dividend or distribution
or for determining rights to vote in respect of any such reorganization,
reclassification, consolidation, merger, sale, lease, conveyance, dissolution,
liquidation or winding-up and (ii) in the case of any such reorganization,
reclassification, consolidation, merger, sale, lease, conveyance, dissolution,
liquidation or winding-up, at least fifteen (15) business days' written notice
of the date when the same shall take place.  Any notice given in accordance with
clause (i) above shall also specify, in the case of any such dividend or
distribution, the record date for such dividend or distribution.  Any notice
given in accordance with clause (ii) above shall also specify the date on which
the holders of Common Stock shall be entitled to exchange their Common Stock for
securities or other property, if any, deliverable upon such reorganization,
reclassification, consolidation/merger, sale, lease, conveyance, dissolution,
liquidation or winding-up, as the case may be and in connection with the
occurrence amount and character of such dividend, distribution, right or other
event described in clause (d) above such notice shall specify the anticipated
net equity value that will accrue to Common Stock holders so that the Holder can
make an informed decision whether or not to exercise this Warrant.  In the event
that the Holder of the Warrant does not exercise this Warrant prior to the
occurrence of an event described in clause (a) or (b) above, the Holder shall
not be entitled to receive the benefits accruing to existing holders of the
Common Stock in such event.  Upon the occurrence of an event described in clause
(c) the Holder shall be entitled thereafter, upon payment of the Stock Purchase
Price in effect immediately prior to such action, to receive upon exercise of
this Warrant, the class and number of shares which the Holder would have been
entitled to receive after the occurrence of such event had this Warrant been
exercised immediately prior to such event.  In connection with the transactions
described in clause (c), the Company will require each person (other than the
Company) that may be required to deliver any cash, stock, securities or other
property upon the exercise of this Warrant, as provided herein, to assume, by
written instrument delivered to the Holder of this Warrant, (x) the obligations
of the Company under this Warrant and (y) the obligation to deliver to such
Holder such cash, stock, securities or other property as such Holder may be
entitled to receive in accordance with the provisions
<PAGE>

of this Section 3. Notwithstanding any other provision hereof, no Holder shall
have the right to obtain an injunction or restraining order or otherwise
interfere with or prevent the occurrence of any of the actions described in (a)-
(d) above.

     4.  Issue Tax.  The issuance of certificates for the Warrant Shares upon
         ---------
the exercise of the Warrant shall be made without charge to the Holder of the
Warrant for any issue tax in respect thereof; provided, however, that the
                                              --------  -------
Company shall not be required to pay any tax which may be payable in respect of
any transfer involved in the issuance and delivery of any certificate in a name
other than that of the then Holder of the Warrant being exercised.

     5.  No Voting or Dividend Rights; Limitation of Liability.  Nothing
         -----------------------------------------------------
contained in this Warrant shall be construed as conferring upon the Holder
hereof the right to vote or to consent or to receive notice as a stockholder in
respect of meetings of stockholders for the election of directors of the Company
or any other matters or any rights whatsoever as a stockholder of the Company.
Except for the adjustment to the Stock Purchase Price pursuant to Section 3.1 in
the event of a dividend on the Common Stock payable in shares of Common Stock,
no dividends or interest shall be payable or accrued in respect of this Warrant
or the interest represented hereby or the shares purchasable hereunder until,
and only to the extent that, this Warrant shall have been exercised.  No
provisions hereof, in the absence of affirmative action by the Holder to
purchase shares of Warrant Shares, and no mere enumeration herein of the rights
or privileges of the Holder hereof, shall give rise to any liability of such
Holder for the Stock Purchase Price or as a stockholder of the Company whether
such liability is asserted by the Company or by its creditors.

     6.  Registration Rights and Indemnification.
         ---------------------------------------

         6.1  Registration Rights. The Warrant Shares shall have the same
              -------------------
registration and other rights granted to those certain purchasers as outlined in
Sections 5.3 and 5.5 of Annex I of the Stock and Warrant Purchase Agreements
dated as of the date hereof.

         6.2  Indemnification and Contribution.
              --------------------------------

              6.2.1  Indemnification by the Company.  The Company agrees to
                     ------------------------------
indemnify and hold harmless the Holder from and against any losses, claims,
damages or liabilities (or actions or proceedings in respect thereof) to which
the Holder may become subject (under the Securities Act or otherwise) insofar as
such losses, claims, damages or liabilities (or actions or proceedings in
respect thereof) arise out of, or are based upon, any claim by a third party
asserting any untrue statement of a material fact contained in the Registration
Statement, on the effective date thereof, or arise out of any failure by the
Company to fulfill any undertaking included in the Registration Statement, and
the Company will, as incurred, reimburse such Holder for any legal or other
expenses reasonably incurred in investigating, defending or preparing to defend
any such action, proceeding or claim; provided, however, that the Company shall
                                      --------  -------
not be liable in any such case to the extent that such loss, claim, damages or
liability arises out of, or is based upon (i) an untrue statement or alleged
untrue statement made in such Registration Statement in reliance upon and in
conformity with written information furnished to the Company by or on behalf of
the Holder specifically for use in preparation of the Registration Statement or
(ii) any untrue statement in any prospectus that is corrected in any subsequent
prospectus that was delivered to the Holder prior to the pertinent sale or sales
by the Holder.

              6.2.2  Indemnification by Holder.  The Holder agrees to indemnify
                     -------------------------
and hold harmless the Company from and against any losses, claims, damages or
liabilities (or actions or proceedings in respect thereof) to which the Company
may become subject (under the Securities Act or otherwise) insofar as such
losses, claims, damages or liabilities (or actions or proceedings in respect
thereof) arise out of, or are based upon any claim by a third party asserting
(i) an untrue statement made in such Registration Statement in reliance upon and
in conformity with written information furnished to the Company by or on behalf
of the
<PAGE>

Holder specifically for use in preparation of the Registration Statement,
provided, however, that no Holder shall be liable in any such case for any
--------  -------
untrue statement included in any Prospectus which statement has been corrected,
in writing, by the Holder and delivered to the Company at least three business
days before the sale from which such loss occurred or (ii) any untrue statement
in any prospectus that is corrected in any subsequent prospectus that was
delivered to the Holder prior to the pertinent sale or sales by the Holder, and
the Holder will, as incurred, reimburse the Company for any legal or other
expenses reasonably incurred in investigating, defending or preparing to defend
any such action, proceeding or claim.

              6.2.3  Indemnification Procedures.  Promptly after receipt by any
                     --------------------------
indemnified person of a notice of a claim or the beginning of any action in
respect of which indemnity is to be sought against an indemnifying person
pursuant to this Section 6.2, such indemnified person shall notify the
indemnifying person in writing of such claim or of the commencement of such
action, and, subject to the provisions hereinafter stated, in case any such
action shall be brought against an indemnified person and the indemnifying
person shall have been notified thereof, the indemnifying person shall be
entitled to participate therein, and, to the extent that it shall wish, to
assume the defense thereof, with counsel reasonably satisfactory to the
indemnified person; provided, however, that the failure of any indemnified party
                    --------  -------
to give notice as provided herein shall not relieve the indemnifying party of
its obligations hereunder unless the failure to give such notice is materially
prejudicial to an indemnifying party's ability to defend such action.  After
notice from the indemnifying person to such indemnified person of the
indemnifying person's election to assume the defense thereof, the indemnifying
person shall not be liable to such indemnified person for any legal expenses
subsequently incurred by such indemnified person in connection with the defense
thereof; provided, however, that if there exists or shall exist a conflict of
         --------  -------
interest that would make it inappropriate in the reasonable opinion of counsel
for the indemnified person for the same counsel to represent both the
indemnified person and such indemnifying person or any affiliate or associate
thereof, the indemnified person shall be entitled to retain its own counsel at
the expense of such indemnifying person; provided, however, that in the case of
                                         --------  -------
the immediately preceding proviso the indemnifying person shall not be
responsible for the legal expenses of more than one counsel for all indemnified
persons.

              6.2.4  Contribution in Lieu of Indemnity.  If the indemnification
                     ---------------------------------
provided for in this Section 6.2 is unavailable to or insufficient to hold
harmless an indemnified party under Section 6.2.1 or 6.2.2 above in respect of
any losses, claims, damages or liabilities (or actions or proceedings in respect
thereof) referred to therein, then the indemnifying party shall contribute to
the amount paid or payable by such indemnified party as result of such losses,
claims, damages or liabilities (or actions in respect thereof), as well as any
other relevant equitable considerations.  The relative fault shall be determined
by reference to, among other things, whether the untrue or alleged untrue
statement of a material fact or the omission or alleged omission to state a
material fact relates to information supplied by the Company on the one hand or
the Holder on the other and the parties' relative intent, knowledge, access to
information and opportunity to correct or prevent such statement or omission.
The Company and the Holder agree that it would not be just and equitable if
contribution pursuant to this Section 6.2.4 were determined by pro rata
allocation or by any other method of allocation which does not take account of
the equitable considerations referred to above in this Section 6.2.4. The amount
paid or payable by an indemnified party as a result of the losses, claims,
damages or liabilities (or actions in respect thereof) referred to above in this
Section 6.2.4 shall be deemed to include any legal or other expenses reasonably
incurred by such indemnified party in connection with investigating or defending
any such action or claim.  Notwithstanding the provisions of this Section 6.2.4,
the Holder shall not be required to contribute any amount in excess of the net
amount received by the Holder from the sale of the Warrant Shares to which such
loss relates.  No person guilty of fraudulent misrepresentation (within the
meaning of Section 11 (f) of the Securities Act) shall be entitled to
contribution from any person who was not guilty of such fraudulent
misrepresentation.  The Holder's obligations in this Section 6.2.4 to contribute
is several in proportion to its respective sales of Warrant Shares to which such
loss relates and not joint.
<PAGE>

              6.2.5  Controlling Persons Indemnified.  The obligations of the
                     -------------------------------
Company and the Holder under this Section 6.2 shall be in addition to any
liability which the Company and the Holders may otherwise have and shall extend,
upon the same terms and conditions, to each person, if any, who controls the
Company or the Holder within the meaning of the Securities Act.

     7.  Restrictions on Transferability of Securities: Compliance With
         --------------------------------------------------------------
Securities Act.
--------------

         7.1  Restrictions on Transferability. The Warrant and the Warrant
              -------------------------------
Shares (collectively, the "Securities") shall not be transferable in the absence
of a registration under the Securities Act or an exemption therefrom, or in the
absence of compliance with any term of the Warrant.  Without limiting the
foregoing, (i) the Securities may be offered, resold, pledged or otherwise
transferred only (A) in a transaction meeting the requirements of Rule 144 of
the SEC ("Rule 144"), or in accordance with another exemption from the
registration requirements of the Securities Act (and based upon an opinion of
counsel if the Company so requests) or (B) pursuant to an effective registration
statement under the Securities Act, in each case in accordance with the
applicable securities laws of any state of the United States or any other
applicable jurisdiction and (ii) Purchaser will be required to notify any
subsequent purchaser of the resale restrictions set forth above.  The Company
shall be entitled to give stop transfer instructions to the transfer agent with
respect to the Securities in order to enforce the foregoing restrictions.

         7.2  Restrictive Legend.  Unless otherwise received in a transaction
              ------------------
registered under the Securities Laws and qualified (if necessary) under
applicable state securities laws, each certificate representing the Securities
or any other securities issued in respect of the Securities upon any stock
split, stock dividend, recapitalization, merger, consolidation or similar event,
shall (unless otherwise permitted by the provisions of the Purchase Agreement)
be stamped or otherwise imprinted with a legend substantially in the following
form (in addition to any legend required under applicable state securities
laws):

         THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE BEEN ACQUIRED FOR
         INVESTMENT AND HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF
         1933, AS AMENDED (THE "SECURITIES ACT"). THE SECURITIES MAY NOT BE
         SOLD, TRANSFERRED, ASSIGNED OR HYPOTHECATED UNLESS REGISTERED UNDER THE
         SECURITIES ACT AND QUALIFIED UNDER APPLICABLE STATE SECURITIES LAWS OR
         UNLESS SUCH SALE, TRANSFER, ASSIGNMENT OR HYPOTHECATION IS EXEMPT FROM
         THE REGISTRATION REQUIREMENTS OF THE SECURITIES ACT AND THE
         QUALIFICATION REQUIREMENTS OF APPLICABLE STATE SECURITIES LAWS AND THE
         COMPANY RECEIVES AN OPINION OF COUNSEL SATISFACTORY TO THE COMPANY THAT
         SUCH REGISTRATION AND QUALIFICATION ARE NOT REQUIRED. THE SECURITIES
         REPRESENTED BY THIS CERTIFICATE AND THE RIGHTS OF HOLDERS THEREOF ARE
         SUBJECT TO CERTAIN RESTRICTIONS ON TRANSFER.

         7.3  Exchange of Warrant.  Subject to the terms and conditions hereof,
              -------------------
including the restrictions on transfer in this Section 7, upon surrender of this
Warrant to the Company with a duly executed Assignment Form in the form attached
hereto and funds sufficient to pay any transfer tax, the Company shall, without
charge, execute and deliver a new Warrant or Warrants of like tenor in the name
of the assignee named in such Assignment Form and this Warrant shall promptly be
canceled; provided, however, that if the transfer is for less than all of this
          --------  -------
Warrant, the transferor shall pay all reasonable costs of the Company in
connection with a transfer of Warrants to purchase less than twenty-five
thousand (25,000) Warrant Shares (in either case as adjusted for any stock
dividend, split, combination, recapitalization or the like with respect to such
shares).  The term "Warrant" as used herein shall be deemed to include any
Warrants issued in exchange for this Warrant.
<PAGE>

         7.4  Ownership of Warrant.  The Company may deem and treat the person
              --------------------
in whose name this Warrant is registered as the holder and owner hereof
(notwithstanding any notations of ownership or writing hereon made by anyone
other than the Company) for all purposes and shall not be affected by any notice
to the contrary, until presentation of this Warrant for registration of transfer
as provided in Section 7.3.

     8.  Representations and Warranties.
         ------------------------------

         8.1  Representations and Warranties of Holders  The Holder hereby
              -----------------------------------------
represents and warrants to the Company as follows:

              8.1.1  Investment Intent.  The Holder is acquiring the Warrants
                     -----------------
for investment for its own account only, not as a nominee or agent, and not with
a view to, or for resale in connection with, any "distribution" of any part
thereof within the meaning of the Securities Act. The Holder has no present
intention of selling, granting any participation in, or otherwise distributing
the same. The Holder does not have any contract, undertaking, agreement or
arrangement with any person to sell, transfer or grant any participation to such
person or to any third person with respect to any of the Securities. The Holder
understands that the Securities have not been registered under the Securities
Act or registered or qualified under any state securities law in reliance on
specific exemptions therefrom, which exemptions may depend upon, among other
things, the bona fide nature of Holder's investment intent as expressed herein.

              8.1.2  Investment Experience.  The Holder (i) has such knowledge
                     ---------------------
and experience in financial and business matters as to be capable of evaluating
the merits and risks of acquiring the Warrant and Warrant Shares; (ii) has
received all of the information that the Holder has requested from the Company
and that the Holder considers necessary or appropriate for deciding whether to
acquire the Warrant and Warrant Shares; (iii) has the ability to bear the
economic risks of the prospective investment; and (iv) is able, without
materially impairing its financial condition, to hold the Warrant and Warrants
Shares for an indefinite period of time and to suffer complete loss on the
investment therein. The Holder is aware of the Company's business affairs and
financial condition and has acquired sufficient information about the Company to
reach an informed and knowledgeable decision to acquire the Securities. The
Holder has such business and financial experience, including without limitation,
investment is technology and biotechnology companies, as will enable the Holder
to fend for itself, make an informed investment decision and protect its own
interests in connection with the purchase of the Securities.

              8.1.3  The Holder understands that the Securities it is acquiring
are characterized as "restricted securities" under the federal securities laws
inasmuch as they are being acquired from the Company in a transaction not
involving a public offering and that under such laws and applicable regulations
such securities may be resold without registration under the Securities Act only
in certain limited circumstances. In this connection, the Holder represents that
it is familiar with Rule 144 promulgated by the SEC under the Securities Act, as
presently in effect, and understands the resale limitations imposed thereby and
by the Securities Act.

         8.2  Survival of Representations and Warranties.  The representations
              ------------------------------------------
and warranties made in Section 8.1 of this Warrant will survive the date of this
Warrant and will expire on the earlier of (i) the Expiration Date or (ii) the
exercise of this Warrant in full.

     9.  Modification and Waiver.  Except as otherwise provided herein, this
         -----------------------
Warrant and any provision hereof may be changed, waived, discharged or
terminated only by an instrument in writing signed by the party against which
enforcement of the same is sought.

     10. Notices.  Except as otherwise provided herein, any notice, request or
         -------
other document required or permitted to be given or delivered to the holder
hereof or the Company shall be delivered or shall
<PAGE>

be sent by United States certified or registered mail, postage prepaid, (or
international delivery service for international deliveries) to Holder at its
address as shown on the books of the Company or to the Company at the address
indicated therefor in the first paragraph of this Warrant.

     11.  Descriptive Headings and Governing Law.  The descriptive headings of
          --------------------------------------
the several sections and paragraphs of this Warrant are inserted for convenience
only and do not constitute a part of this Warrant.  This Warrant shall be
construed and enforced in accordance with, and the rights of the parties shall
be governed by, the laws of the State of California (without regard to its
conflicts of law provisions).  The Holder hereby irrevocably submits to the
jurisdiction of any State or United States Federal court sitting in the Alameda
or San Francisco counties in the State of California over any action or
proceeding arising out of or relating to this Warrant or any agreement
contemplated hereby, and the Holder irrevocably agrees that all claims in
respect of such action or proceeding may be heard and determined in such State
or Federal court.  The Holder further waives any objection to venue in such
State and any objection to an action or proceeding in such State based on non-
convenient forum.  The Holder further agrees that any action or proceeding
brought against the Company shall be brought only in the State or United States
Federal courts sitting in Alameda or San Francisco counties in the State of
California.  THE HOLDER AGREES TO WAIVE ITS RIGHTS TO A JURY TIRAL OR ANY CLAIM
FOR CAUSE OF ACTION BASED UPON OR ARISING OUT OF THIS WARRANT.

     12.  Lost Warrants or Stock Certificates.  The Company represents and
          -----------------------------------
warrants to Holder that upon receipt of evidence reasonably satisfactory to the
Company of the loss, theft, destruction, or mutilation of any Warrant or stock
certificate and, in the case of any such loss, theft or destruction, upon
receipt of an indemnity and, if requested, bond reasonably satisfactory to the
Company, or, in the case of any such mutilation, upon surrender and cancellation
of such Warrant or stock certificate, the Company at its expense will make and
deliver a new Warrant or stock certificate, of like tenor, in lieu of the lost,
stolen, destroyed or mutilated Warrant or stock certificate.

     13.  Amendment.  This Warrant may be amended only with the written approval
          ---------
of the Company and the Holder of this Warrant.

     14.  Binding Effect; Benefits.  This Warrant shall inure to the benefit of
          ------------------------
and shall be binding upon the Company and the Holder and their respective heirs,
legal representatives, successors and assigns.  Nothing in this Warrant,
expressed or implied, is intended to or shall confer on any person other than
the Company and the Holder, or their respective heirs, legal representatives,
successors or assigns, any rights, remedies, obligations or liabilities under or
by reason of this Warrant.

     15.  Fractional Shares.  No fractional shares shall be issued upon exercise
          -----------------
of this Warrant.  The Company shall, in lieu of issuing any fractional share,
pay the Holder entitled to such fraction a sum in cash equal to such fraction
multiplied by the market price of the Common Stock on such exercise date, which
shall be, on such date, the closing price for the Common Stock or the closing
bid if no sales were reported, as quoted on the exchange or market that is the
primary trading market for the Company.

     IN WITNESS WHEREOF, the Company has caused this Warrant to be executed by
its officers, thereunto duly authorized this 3rd day of May, 2001.

                              CARDIMA, INC., a Delaware corporation

                              By: ________________________________________
                                    Name: Ronald E. Bourquin
                                    Title: Chief Financial Officer
<PAGE>

ACKNOWLEDGED AND ACCEPTED:

By: ______________________________

    Name: ________________________
<PAGE>

                              FORM OF SUBSCRIPTION
                              --------------------

                  (To be signed only upon exercise of Warrant)

To:  Cardima, Inc.

     The undersigned, the holder of the within Warrant, hereby irrevocably
elects to exercise such Warrant for, and to purchase thereunder,
________________ (________) shares of Common Stock of Cardima, Inc. (the
"Company"), and

     tenders herewith payment in the amount of $________ therefor or

     elects to exercise such Warrant pursuant to the net issuance provisions
provided for in Section 1.3 thereof.   (PLEASE CHECK THE APPROPRIATE FORM OF
PAYMENT).

     The certificates for such shares should be issued in the name of, and
delivered to, _______________

whose address is _______________________________________________________________

__________________________________________________________.

     The undersigned represents, unless the exercise of this Warrant has been
registered under the Securities Act of 1933, as amended (the "Securities Act"),
that (i) the undersigned is acquiring such Common Stock for his or its own
account for investment and not with a view to or for sale in connection with any
distribution thereof (except for any resale pursuant to a registration statement
under the Securities Act), (ii) the undersigned has such knowledge and
experience in financial and business matters as to be capable of evaluating the
merits and risks of the undersigned's investment in the shares of Common Stock,
(iii) the undersigned has received all of the information the undersigned
requested from the Company and the undersigned considers necessary or
appropriate for deciding whether to purchase the shares, (iv) the undersigned
has the ability to bear the economic risks of the undersigned's prospective
investment and (v) the undersigned is able, without materially impairing his
financial condition, to hold the shares of Common Stock for an indefinite period
of time and to suffer complete loss on the undersigned's investment.

     Please issue a new Warrant for the unexercised portion of the attached
Warrant in the name of the undersigned or in such other name as is specified
here __________________________________________.

DATED: _______________________

                                __________________________________________
                                (Signature must conform in all respects to
                                name of holder as specified on the face of
                                the Warrant)

                                __________________________________________
                                __________________________________________
                                (Address)
<PAGE>

THIS WARRANT AND ANY SHARES ACQUIRED UPON THE EXERCISE OF THIS WARRANT HAVE NOT
BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, AND MAY NOT BE
SOLD OR OTHERWISE TRANSFERRED EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION
STATEMENT FILED UNDER SUCH ACT OR PURSUANT TO AN EXEMPTION FROM REGISTRATION
UNDER SUCH ACT.

                                ASSIGNMENT FORM
                                ---------------

              (To be executed only upon transfer of this Warrant)

     For value received, the undersigned registered holder of the within Warrant
hereby sells, assigns and transfers unto ____________________ (the "Assignee")
the right represented by such Warrant to purchase __________ Warrant Shares and
all other rights of the Holder with respect thereto under the within Warrant,
and appoints _________________ as Attorney to make such transfer on the books of
Cardima, Inc. maintained for such purpose, with full power of substitution in
the premises.

     The undersigned also represents that, by assignment hereof, the Assignee
acknowledges that this Warrant and the Warrant Shares to be issued upon exercise
hereof are being acquired for investment and that the Assignee will not offer,
sell or otherwise dispose of this Warrant or any Warrant Shares to be issued
upon exercise hereof except under circumstances that will not result in a
violation of the Securities Act of 1933, as amended, or any state securities
laws.  Further, the Assignee has acknowledged that upon exercise of this
Warrant, the Assignee shall, if requested by the Company, confirm in writing, in
a form satisfactory to the Company, that the Warrant Shares so purchased are
being acquired for investment and not with a view toward distribution or resale.

Dated:  ____________________.

                                         __________________________________
                                                     (Signature)

                                         __________________________________
                                                     (Print Name)

                                         __________________________________
                                                   (Street Address)

                                         __________________________________
                                         (City)      (State)     (Zip Code)

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