Amegy Bancorporation (ABNK) 10-K 2003 FY Annual report

EXHIBIT 32.1

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

     Pursuant to Section 1350, Chapter 63 of Title 18, United States Code, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, the undersigned, as Chief Executive Officer of Southwest Bancorporation of Texas, Inc. (the “Company”), does hereby certify that:

     1)     the Company’s Annual Report on Form 10-K for the year ended December 31, 2003 (the “Report”), fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

     2)     the information contained in the Company’s Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Dated: February 24, 2004

/s/ PAUL B. MURPHY, JR.

Paul B. Murphy, Jr.

Director and Chief Executive Officer