<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)