Exhibit 32.1

CERTIFICATION WITH RESPECT TO
QUARTERLY REPORT OF
HCC INSURANCE HOLDINGS, INC.

The undersigned, being the Chief Executive Officer and Chief Financial Officer of HCC Insurance Holdings, Inc. (the “Company”), pursuant to 18 U.S.C. § 1350 as adopted pursuant to §906 of the Sarbanes-Oxley Act of 2002, do hereby certify to the best of their knowledge with respect to the Quarterly Report of the Company on Form 10-Q, as filed with the Securities and Exchange Commission for the quarter ended March 31, 2005 (the “Report”):

1.	that the Report fully complies with all requirements of Section 13(a) and 15(d) of the Securities Exchange Act of 1934, as amended; and
2.	that the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company as of and for the periods presented in the Report.

May 9, 2005	/s/ Stephen L. Way
(Date)	Stephen L. Way, Chairman of the Board, Chief Executive Officer and President
May 9, 2005	/s/ Edward H. Ellis, Jr.
(Date)	Edward H. Ellis, Jr., Executive Vice President and Chief Financial Officer

A signed original of this written statement required by §906 has been provided to HCC Insurance Holdings, Inc. and will be retained by HCC Insurance Holdings, Inc. and furnished to the Securities and Exchange Commission or its staff upon request.