<PAGE>

                                  [LETTERHEAD]


                                                                  CONFIDENTIAL
                                                                  ------------

March 24, 1998


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

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

Dear Charlie:

This letter agreement sets forth the terms and conditions under which 
Conductus, Inc. ("Conductus" or the "Company") has retained Sutro & Co. 
Incorporated ("Sutro") to act as its exclusive 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 - Sutro 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)  Advising the Company as to the form and structure of the Financing;

     (b)  Assisting in the preparation of a Private Placement Memorandum (the 
          "Memorandum") describing the Company, the transaction and the 
          securities offered in connection therewith (the "Securities"). 
          Responsibility for the contents of such Memorandum shall be solely 
          that of the Company, and the Memorandum shall not be made available 
          to or used in discussions with prospective investors (the "Party" 
          or "Parties") by Sutro until both the Memorandum and its use for 
          that purpose have been approved by the Company;

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

     (d)  Negotiating the sale of the Securities to investors;

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

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<PAGE>

2.   RETAINER - Sutro shall be paid a nonrefundable retainer in the amount of 
     $25,000 which shall be deemed compensation hereunder and which shall be 
     credited against any fees payable pursuant to paragraph 3(a) upon 
     completion of the Financing.

3.   COMPENSATION - Upon completion of the Financing, the Company agrees to 
     pay Sutro:

     (a)  A cash placement fee (the "Placement Fee") equal to the greater of 
     $200,000 or six percent (6%) of the Securities sold to new investors and 
     three percent (3%) of the Securities to sold to existing shareholders and 
     certain investors listed on Attachment A. The Placement Fee is paid upon 
     consummation of, and out of the proceeds of, the proposed Financing. 
     Notwithstanding the above, Sutro will not be due a Placement Fee on the 
     first $400,000 raised from Asset Management Company or on Securities sold 
     to current Directors of the Company. 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.

4.   SUTRO'S EXPENSES - In addition to the foregoing fees, and regardless of 
     whether the Financing contemplated by this letter agreement is 
     consummated, the Company agrees, upon request from time to time, to 
     promptly reimburse Sutro for all reasonable out-of-pocket expenses up to 
     limit of $25,000, including, but not limited to, such costs as 
     (i) printing, telephone, fax, courier service, copying, accommodations,  
     travel, and direct computer expenses, secretarial overtime and fees and 
     (ii) disbursements of legal counsel, if required. In the event, the 
     above expenses exceed $25,000; the Company will approve expenses in 
     advance, which approval shall not be unreasonably withheld.

5.   TERM AND TERMINATION RIGHTS - It is understood that the Company hereby 
     engages Sutro on an exclusive basis for investment banking services 
     relating to the Financing for a term (the "Term") commencing on the date 
     hereof and ending on September 30, 1998. The Term shall be automatically 
     renewed for successive 30 day periods unless either party gives written 
     notice to the other within 30 days of the expiration of the Term of its 
     desire that this engagement expire.

     Notwithstanding the foregoing, either Sutro or the Company may terminate 
     its obligation hereunder without liability if, in the reasonable opinion 
     of either party, a change has occurred in the Company's financial 
     condition, results of operations, properties, business prospects, or the 
     composition of the Company's management or Board of Directors, which has 
     adversely effected the marketability of the Company. The remaining 
     provisions of this letter relating to the payment of expenses incurred 
     prior to the end of the Term and the Indemnification Agreement shall 
     survive any termination or expiration of the engagement.

                                     2 of 4
<PAGE>

     If during the Term, or within the six months following the expiration 
     thereof, (a) a financing transaction or transactions occur for the 
     benefit of the Company which involves a Party (i) identified to the 
     Company by Sutro or (ii) with whom the Company or Sutro had a discussion 
     regarding the Financing during the engagement and whether or not such 
     discussions were initiated by Sutro, or (b) the Company enters into a 
     definitive agreement with any such Party specified in (i) or (ii) above 
     which subsequently results in a financing transaction or transactions, 
     then the Company will be obligated to pay Sutro the fees and expenses of 
     Sections 3 and 4.

6.   SALE TRANSACTION - If during the Term, the Company consummates a Sale 
     Transaction (as defined below) or reaches a definitive agreement which 
     subsequently results in a Sale Transaction, the Company agrees to pay or 
     cause to be paid to Sutro, a sale transaction fee (the "Sale Transaction 
     Fee") equal to the lesser of three percent (3%) of the Aggregate 
     Consideration (as defined below) or $750,000. The Sale Transaction Fee 
     will be payable in cash upon the closing of the Sale Transaction.

     The term "Sale Transaction" shall be defined to include any merger, 
     consolidation, sale of assets, tender or exchange offer, leveraged 
     buy-out, formation of a joint venture or partnership, reorganization or 
     other business combination, pursuant to which the business of the 
     Company is combined with that of an acquiring entity or any entity 
     affiliated with one or more acquirers (the "Party" or "Parties"), where 
     the Party has at least 50% of the capital stock of the surviving company.

     The term "Aggregate Consideration" shall be defined to include cash, 
     equity securities, the fair market value of revolving credit facilities, 
     straight and convertible debt instruments or other obligations, and any 
     other form of payment or assumption of obligations made to the Company 
     or its shareholders in connection with the Sale Transaction. If any of 
     the consideration to be received by the Company is contingent upon 
     future performance of the Company's operations (e.g. revenues or 
     income), the portion of the fee attributable to such consideration shall 
     be paid to Sutro at such time or times as the Company receives such 
     consideration.

7.   DUE DILIGENCE - In connection with Sutro's engagement, the Company and 
     its advisors will furnish Sutro with all data, material, and information 
     concerning the Company (the "Information") which Sutro 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, Sutro will be using and relying on the Information and 
     financial and other information furnished to Sutro by potential 
     interested Parties, without independent verification. Moreover, Sutro 
     will not perform any appraisal of the assets or businesses of the 
     Company or any Party. Sutro is hereby authorized to use and deliver the 
     Information, and any other data obtained by Sutro from reliable 
     published sources, to prospective interested Parties. In connection with 
     the engagement of Sutro hereunder, the Company has entered into a 
     separate letter agreement, dated as of the date hereof, providing for 
     the indemnification of Sutro and certain related parties by the Company 
     (the "Indemnification Agreement").

8.   RIGHT OF FIRST REFUSAL - The Company will provide Sutro with the right 
     of first refusal for one year to serve as a managing underwriter on any 
     public or private financing (debt or equity), or act as an advisor on 
     any merger, business combination, recapitalization or sale of some or 
     all of the equity or assets of the Company (collectively, "Future 
     Services"). In the event the Company notifies Sutro of its intention to 
     pursue an activity that would enable Sutro to exercise its right of 
     first refusal to provide Future Services, Sutro shall notify the Company 
     of its election to provide such Future Services,

                                     3 of 4
<PAGE>

     including notification of the compensation and other terms to which 
     Sutro claims to be entitled, within twenty (20) days of written notice 
     by the Company. In the event Sutro is engaged by the Company to provide 
     such Future Services, Sutro will be compensated as is reasonable and 
     customary within the industry PROVIDED; HOWEVER, that the terms of the 
     Indemnification Agreement shall apply to any additional engagement.

9.   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.

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

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

                                       Very truly yours,

                                       SUTRO & CO. INCORPORATED



                                       By:  /s/ John M. Morris
                                           ---------------------------------
                                           John M. Morris
                                           Managing Director


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


                                     4 of 4
<PAGE>

                                  [LETTERHEAD]


                                  Attachment A

                                      [*]






[*]  CONFIDENTIAL TREATMENT REQUESTED. CONFIDENTIAL PORTION HAS BEEN FILED 
     SEPARATELY WITH THE SECURITIES AND EXCHANGE COMMISSION.

<PAGE>

                                                                  CONFIDENTIAL
                                                                  ------------


March 24, 1998

Sutro & Co. Incorporated
11150 Santa Monica Blvd.
Suite 1500
Los Angeles, CA 90025


Gentlemen:

In consideration of Sutro'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 Sutro, its affiliates, the respective 
partners, directors, officers, agents and employees of Sutro and its 
affiliates and each person, if any, controlling Sutro 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, (Sutro 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 Sutro'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 Sutro 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 Sutro 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.

                                    1 of 3
<PAGE>

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 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  
Sutro 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 Sutro 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 Sutro 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 Sutro pursuant to the engagement 
letter. The respective relative benefits received by Sutro and the Company in 
connection with the transaction shall be deemed to be in the same proportion 
as the aggregate fee paid to Sutro in connection with the transaction bears 
to the total consideration of the transaction. The relative fault of Sutro 
and the Company shall be determined by reference to, among other things, 
whether the actions or omissions to act were by Sutro or the Company and the 
parties' relative intent, knowledge, access to information and opportunity to 
correct or prevent such action or omission to act.

                                    2 of 3
<PAGE>

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 matter 
referred to in this letter except to the extent that any such liability 
results from the gross negligence or willful misconduct of Sutro 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 Sutro 
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:

SUTRO & CO. INCORPORATED


By:  /s/ John M. Morris
    -------------------------------
    John M. Morris
    Managing Director



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