Endurance Specialty (ENH) 10-Q 2004 Q1 Quarterly report

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 September 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: May 6, 2004	By:	/s/ Kenneth J. LeStrange
		Kenneth J. LeStrange
		Chief Executive Officer
Date: May 6, 2004	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.