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