<PAGE>

                                                                    CONFIDENTIAL
September 2, 1998



Conductus, Inc.
969 West Maude Avenue
Sunnyvale, California 94086

Attention:  Mr. Charles E. Shalvoy, President and Chief Executive Officer

Dear Mr. Shalvoy:

This letter agreement sets forth the terms and conditions under which Conductus,
Inc. ("Conductus" or the "Company") has retained Davenport & Company LLC
("Davenport") to act as its financial advisor with respect to the private
placement (the "Financing") of equity or equity-related securities (the
"Securities") on a best efforts basis on terms satisfactory to the Company and
in compliance with Section 4(2) of the Securities Act of 1933 as amended, and
other federal and state securities laws.

1.   SERVICES TO BE RENDERED - Davenport will assist the Company in effecting
     the Financing on the terms and conditions of this letter agreement.  In
     this regard, we propose to undertake certain activities including, if
     appropriate, the following:

     (a)  Identify, introducing to, and consulting as to strategy for initiating
          discussions with, potential investors;

     (b)  Negotiating the sale of the Securities to investors; and

     (c)  Assisting in the preparation of definitive documentation for the
          Financing.

2.   COMPENSATION - Upon completion of the Financing the Company agrees to pay
     Davenport a cash placement fee (the "Placement Fee") equal to four percent
     (4%) of the Securities sold to investors identified to the Company by
     Davenport.  The Placement Fee is paid upon consummation of, and out of the
     proceeds of, the proposed Financing. The Placement Fee will be payable
     regardless of the size of the Financing and whether or not the Financing
     occurs in one transaction or a series of transactions.

3.   DUE DILIGENCE - In connection with Davenport's engagement, the Company and
     its advisors will furnish Davenport with all data, material, and
     information concerning the Company (the "Information") which Davenport
     reasonably requests, all of which will be accurate and complete in all
     material respects, except with respect to the Company's financial
     statements which shall present fairly the financial position of the
     Company, to the best of the Company's knowledge, at the time furnished.
     The Company recognizes and confirms that in advising it and in undertaking
     the assignment, Davenport will be using and relying on the Information and
     financial and other information furnished to Davenport by the Company and
     its advisors, without independent verification.  Moreover, Davenport will
     not perform any appraisal of the assets or businesses of the 

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Conductus, Inc.
September 2, 1998
Page 2

     Company or any party.  Davenport is hereby authorized to use and deliver 
     the Information, and any other data obtained by Davenport from reliable 
     published sources to prospective interested investors.  In connection with 
     the engagement of Davenport hereunder, the Company has entered into 
     separate letter agreement, dated as of the date hereof, providing for the 
     indemnification of Davenport and certain related parties by the Company 
     (the "Indemnification Agreement").

4.   CALIFORNIA LAW - This letter agreement and the related indemnification
     agreement referred to above shall be deemed made in California.  Such
     agreements shall be governed by the laws of the state of California,
     without regard to such state's rules concerning conflicts of laws.  Should
     suit be brought to enforce this letter agreement or the Indemnification
     Agreement, the prevailing party shall be entitled to recover from the other
     reimbursement for reasonable attorneys' fees.  Any dispute arising from the
     interpretation, validity or performance of this letter agreement or any of
     its terms and provisions shall be submitted to binding arbitration with the
     National Association of Securities Dealers.

5.   Upon execution of this engagement letter, Davenport and the Company will
     exchange mutually acceptable Confidentiality Agreements.

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Conductus, Inc.
September 2, 1998
Page 3

Please confirm that the foregoing correctly sets forth our agreement by signing
and returning to us the enclosed duplicate copy of this letter agreement.  We
look forward to working with you and to the successful conclusion of this
assignment.

                                        Very truly yours,

                                        DAVENPORT & COMPANY LLC



                                        By: /s/ Robert F. Mizell
                                           ----------------------------------
                                        Name: Robert F. Mizell
                                             --------------------------------
                                        Title: Vice President
                                              -------------------------------
Accepted and Agreed to
as of the date written above:


CONDUCTUS, INC.



By: /s/ Charles E. Shalvoy
   -------------------------------------
   Charles E. Shalvoy
   President and Chief Executive Officer

<PAGE>

                                                                    CONFIDENTIAL


September 2, 1998


Davenport & Company LLC  ("Davenport")
901 E. Cary Street, 11th Floor
Richmond, VA  23219

Gentlemen:

In consideration of Davenport's agreement to act on behalf of Conductus, Inc.
(the "Company"), in connection with the private placement, pursuant to the
engagement letter of even date herewith (the "Engagement Letter"), we hereby
agree to indemnify and hold harmless Davenport, its affiliates, the respective
partners, directors, officers, agents and employees of Davenport and its
affiliates and each person, if any, controlling Davenport or any of its
affiliates within the meaning of either Section 15 of the Securities Act of 1933
or Section 20 of the Securities Exchange Act of 1934, (Davenport and each such
other person are hereinafter referred to as an "Indemnified Person"), from and
against any such losses, claims, damages, expenses and liabilities (or actions
in respect thereof), joint or several, as they may be incurred (including all
legal fees and other expenses incurred in connection with investigating,
preparing, defending, paying, settling, or compromising any claim, action, suit,
proceeding, loss, damage, expense or liability, whether or not in connection
with an action in which any Indemnified Person is a named party) to which any of
them may become subject (including in settlement of any action, suit or
proceeding, if such settlement is effected with the Company's consent, which
consent shall not be unreasonably withheld), and which are related to or arise
out of Davenport's engagement, the transaction contemplated by such engagement
or any Indemnified Person's role in connection therewith, including, but not
limited to, any losses, claims, damages, expenses and liabilities (or actions in
respect thereof) arising out of, based upon or caused by any untrue statement or
alleged untrue statement of a material fact contained in the offering
memorandum, or any amendment or supplement thereto, or in any other document of
the Company furnished to any party or to Davenport in connection with the
Financing Transaction, or arising out of, based upon or caused by any omission
or alleged omission to state in any of them a material fact required to be
stated therein or necessary to make the statements in any of them not
misleading.  The Company will not, however, be responsible under the foregoing
provisions with respect to any loss, claim, damage, expense or liability to the
extent that a court having jurisdiction shall have determined by a final
judgment (not subject to further appeal) that such loss, claim, damage, expense
or liability resulted from actions taken or omitted to be taken by Davenport due
to its gross negligence or willful misconduct.  All capitalized terms not
otherwise defined herein have the same meaning as ascribed to them in the
Engagement Letter, unless the context indicates or requires otherwise.

Promptly after receipt by an Indemnified Person of notice of the commencement of
any action, such Indemnified Person will, if a claim in respect thereof is to be
made against the Company, notify the Company of the commencement thereof; but
the omission to notify the Company will

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Davenport & Company LLC
September 2, 1998
Page 2

not relieve it from any liability which it may have to any Indemnified Person
otherwise than stated in this Indemnification Agreement.  In case any such
action is brought against any Indemnified Person, and it notifies the Company of
the commencement thereof, the Company will be entitled to participate therein
and, to the extent that it may wish, to assume the defense thereof, with counsel
reasonably satisfactory to such Indemnified Person; provided, however, that if
the defendants in any such action include both the Indemnified Person and the
Company and counsel for the Indemnified Person reasonably determines there is a
conflict of interest that cannot or should not be waived, the Company shall not
have the right to direct the defense of such action on behalf of such
Indemnified Person and such Indemnified Person shall have the right to select
separate counsel to defend such action on behalf of such Indemnified Person.
After notice from the Company to such Indemnified Person of its election to
assume the defense thereof and approval by such Indemnified Person of counsel
appointed to defend such action, the Company will not be liable to such
Indemnified Person for any legal or other expenses, other than reasonable costs
of investigation, incurred by such Indemnified Person in connection with the
defense thereof unless: (i) the Indemnified Person shall have employed separate
counsel in accordance with the proviso to the next preceding sentence (it being
understood, however, that in connection with such action the Company shall not
be liable for the expenses of more than one separate counsel (in addition to
local counsel) in any one action or separate but substantially similar actions
in the same jurisdiction arising out of the same general allegations or
circumstances); or (ii) the Company has authorized the employment of counsel for
the Indemnified Person at the expense of the Company.  After any notice from the
Company to such Indemnified Person, the Company will not be liable for the costs
and expenses of any settlement of such action effected by such Indemnified
Person without the consent of the Company.

If the indemnity referred to above should be, for any reason whatsoever,
unenforceable, unavailable to or otherwise insufficient to hold harmless
Davenport and each Indemnified Person in connection with the transaction, each
Indemnified Person shall be entitled to receive from the Company, and the
Company shall pay, contributions for such losses, claims, damages, liabilities
and expenses (or actions in respect thereof) so that each Indemnified Person
ultimately bears only a portion of such losses, claims, damages, liabilities
expenses and actions as is appropriate (i) to reflect the relative benefits
received by Davenport on the one hand and the Company on the other hand in
connection with the transaction or (ii) if the allocation on that basis is not
permitted by applicable law, to reflect not only the relative benefits referred
to in clause (i) above but also the relative fault of Davenport and the Company
in connection with the actions or omissions to act which resulted in such
losses, claims, damages, liabilities or expenses, as well as any other relevant
equitable considerations; provided, however, that in no event shall the
aggregate contribution of all Indemnified Persons to all losses, claims,
damages, liabilities, expenses and actions exceed the amount of the fee actually
received by Davenport pursuant to the engagement letter.  The respective
relative benefits received by Davenport and the Company in connection with the
transaction shall be deemed to be in the same proportion as the aggregate fee
paid to Davenport in connection with the transaction bears to the total
consideration of the transaction.  The relative fault of Davenport and the
Company shall be determined by reference to, among other things, whether the
actions or omissions to act were by Davenport or the Company and the 

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Davenport & Company LLC
September 2, 1998
Page 3

parties' relative intent, knowledge, access to information and opportunity to 
correct or prevent such action or omission to act.

The indemnity, contribution and expense payment obligations of the Company
referred to above shall be in addition to any liability which the Company may
otherwise have and shall be binding upon and inure to the benefit of any
successors, assigns, heirs and personal representatives of any Indemnified
Person and the Company.  The Company also agrees that the Indemnified Persons
shall have no liability to the Company or any person asserting claims on behalf
of or in right of the Company for or in connection with any manner referred to
in this letter except to the extent that any such liability results from the
gross negligence or willful misconduct of Davenport in performing the services
that are the subject of this letter and in no event shall such liability exceed
the amount of fees actually received by Davenport hereunder.


                              Very truly yours,

                              CONDUCTUS, INC.



                              By: /s/ Charles E. Shalvoy
                                 -------------------------------------
                                 Charles E. Shalvoy
                                 President and Chief Executive Officer

Accepted and Agreed to
as of the date written above:

DAVENPORT & COMPANY LLC



By: /s/ Robert F. Mizell       
   ----------------------------
Name: Robert F. Mizell         
     --------------------------
Title: Vice President          
      -------------------------