<PAGE>
                                                                     Exhibit 4.1




      [GRAPHIC OF SEAL OF ENDURANCE SPECIALTY HOLDINGS LTD., BERMUDA 2002]




ORDINARY SHARES                                               ORDINARY SHARES

ORGANIZED UNDER THE LAWS
      OF BERMUDA                   [ENDURANCE LOGO]              SHARES



   THIS CERTIFICATE IS TRANSFERABLE
IN NEW YORK, NY, JERSEY CITY, NJ, CANTON, MA
          AND HAMILTON, BERMUDA


                                                               CUSIP G30397 10 6
                                             SEE REVERSE FOR CERTAIN DEFINITIONS


                       ENDURANCE SPECIALTY HOLDINGS LTD.


THIS IS TO CERTIFY THAT




IS THE REGISTERED HOLDER OF


FULLY PAID AND NON-ASSESSABLE ORDINARY SHARES, PAR VALUE US $1.00 PER SHARE, OF


Endurance Specialty Holdings Ltd. transferable on the books of the Company by
the holder hereof in person or by duly authorized attorney upon surrender of
this certificate properly endorsed. This certificate and the shares represented
hereby are issued and shall be held subject to all the provisions of the
Memorandum of Association and the Amended and Restated Bye-Laws of the Company,
copies of which are on file with the Transfer Agent, to all of which the
holder by acceptance hereof assents.


     This certificate is not valid unless countersigned and registered by the
Transfer Agent and Registrar.

     Witness the seal of the Company and the signatures of its duly authorized
officers.

Dated

COUNTERSIGNED AND REGISTERED:

       EQUISERVE TRUST COMPANY, N.A.

                              TRANSFER AGENT
                               AND REGISTRAR

BY


                          AUTHORIZED OFFICER






                                   SECRETARY




                      CHAIRMAN, PRESIDENT AND
                      CHIEF EXECUTIVE OFFICER



<PAGE>
                       ENDURANCE SPECIALTY HOLDINGS LTD.

     The following abbreviations, when used in the inscription on the face of
this certificate, shall be construed as though they were written out in full
according to applicable laws or regulations:

<Table>
<S>                                                     <C>
  TEN COM -- as tenants in common                       UNIF GIFT MIN ACT -- ...........Custodian................
  TEN ENT -- as tenants by the entireties                                    (Cust)                 (Minor)
  JT TEN  -- as joint tenants with right of                                  under Uniform Gifts to Minors
                survivorship and not as tenants                              Act ................................
                in common                                                            (State)
</Table>

     Additional abbreviations may also be used though not in the above list.

For value received, ______________ hereby sell, assign and transfer unto
PLEASE INSERT SOCIAL SECURITY OR OTHER
  IDENTIFYING NUMBER OF ASSIGNEE
______________________________________
|                                    |
|                                    |
______________________________________


________________________________________________________________________________
  (PLEASE PRINT OR TYPEWRITE NAME AND ADDRESS, INCLUDING ZIP CODE, OF ASSIGNEE)

________________________________________________________________________________


________________________________________________________________________________


_________________________________________________________________________ shares
represented by the within certificate, and do hereby irrevocably constitute and
appoint

_______________________________________________________________________ Attorney
to transfer the said shares on the books of the within named Company with full
power of substitution in the premises.

Dated ___________________________




               _________________________________________________________________
       NOTICE: THE SIGNATURE TO THIS ASSIGNMENT MUST CORRESPOND WITH THE NAME AS
               WRITTEN UPON THE FACE OF THE CERTIFICATE IN EVERY PARTICULAR,
               WITHOUT ALTERATION OR ENLARGEMENT OF ANY CHANGE WHATEVER.


Signature(s) Guaranteed:


____________________________________________________________________
THE SIGNATURE(S) MUST BE GUARANTEED BY AN ELIGIBLE GUARANTOR
INSTITUTION (BANKS, STOCKBROKERS, SAVINGS ASSOCIATIONS AND CREDIT
UNIONS WITH MEMBERSHIP IN AN APPROVED SIGNATURE GUARANTEE MEDALLION
PROGRAM), PURSUANT TO S.E.C. RULE 17Ad-15.