EXHIBIT 32

                CERTIFICATION PURSUANT TO 18 U.S.C SECTION 1350,
                                  AS ENACTED BY
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with Third Wave Technologies, Inc. (the "Company) Form 10-Q for
the period ended March 31, 2005 as filed with the Securities and Exchange
Commission on the date hereof (the "Report"), John Puisis, Chief Executive
Officer of the Company, and James Herrmann, Principal Financial Officer of 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 Quarterly Report on Form 10-Q (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 this Report fairly presents, in all
material respects, the financial condition and result of operations of the
Company.

                                     /s/ John Puisis
                                     -------------------------------------------
                                     John Puisis
                                     Chief Executive Officer
                                     May 10, 2005

                                     /s/ James Herrmann
                                     -------------------------------------------
                                     James Herrmann
                                     Principal Financial Officer
                                     May 10, 2005

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