Exhibit 32

                        Endurance Specialty Holdings Ltd.

                      CERTIFICATION PERSUANT TO SECTION 906
                        OF THE SARBANES-OXLEY ACT OF 2002

      In connection with the Quarterly Report on Form 10-Q of Endurance
Specialty Holdings Ltd. (the "Company") for the quarterly period ended June 30,
2003 as filed with the Securities and Exchange Commission on the date hereof
(the "Report"), the undersigned, in the capacities and on the dates indicated
below, each hereby certify pursuant to 18 U.S.C. section 1350, as adopted
pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that (1) to the best
of his knowledge the Report fully complies with requirements of Section 13(a) or
15(d) of the Securities Exchange Act of 1934 and (2) the information contained
in the Report fairly presents, in all material respects, the financial condition
and results of operations of the Company.


Date: August 13, 2003                   By: /s/ Kenneth J. LeStrange
                                            ------------------------------------
                                            Kenneth J. LeStrange
                                            Chief Executive Officer


Date: August 13, 2003                   By: /s/ James R. Kroner
                                            ------------------------------------
                                            James R. Kroner
                                            Chief Financial Officer

This certification accompanies the Report pursuant to Section 906 of the
Sarbanes-Oxley Act of 2002 and shall not, except to the extent required by the
Sarbanes-Oxley Act of 2002, be deemed filed by the Company for purposes of
Section18 of the Securities Exchange Act of 1934, as amended.


                                       55