EXHIBIT 32.1

CERTIFICATION PURSUANT TO 18 U.S.C. SECTION 1350,
OF CHAPTER 63 OF TITLE 18
OF THE UNITED STATES CODE

I, Kevin T. Conroy, President and Chief Executive Officer of Third Wave Technologies, Inc. (the “Company”), certify, pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, 18 U.S.C. Section 1350, that on the date of this Certification:

1. the Annual Report on Form 10-K of the Company for the annual period ended December 31, 2005, (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 results of operations of the Company.

/s/   Kevin T. Conroy

Kevin T. Conroy

Date: March 9, 2006