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

In connection with this Annual Report of Integrated Electrical Services, Inc. (the “Company”) on Form 10-K for the period ending September 30, 2004 (the “Report”), I, Herbert R. Allen, Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. ss. 1350, as adopted pursuant to ss. 906 of the Sarbanes-Oxley Act of 2002, that:

(1) 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 Report fairly presents, in all material respects, the financial condition and result of operations of the Company.

/s/    HERBERT R. ALLEN        

Herbert R. Allen

Chief Executive Officer and

Interim Chief Financial Officer

December 14, 2004