Exhibit 32.02

      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 the Quarterly  Report of Concord  Communications,  Inc. (the
"Company") on Form 10-Q for the period  ending  September 30, 2004 as filed with
the Securities  and Exchange  Commission on the date hereof (the  "Report"),  I,
Melissa H. Cruz,  Executive Vice President,  Business Services,  Chief Financial
Officer and  Treasurer of the Company,  certify,  pursuant to 18 U.S.C.  Section
1350,  as adopted  pursuant  to Section 906 of the  Sarbanes-Oxley  Act of 2002,
that, to the best of my knowledge:

      (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 results of operations of the
Company.

Melissa H. Cruz
Executive Vice President, Business Services,
Chief Financial Officer and Treasurer
November 5, 2004

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