Exhibit 99.1

Certification of Chief Executive Officer

pursuant to 18 U.S.C. §1350 adopted pursuant to

Section 906 of the Sarbanes-Oxley Act of 2002

I, Harry J. Carr, hereby certify pursuant to 18 U.S.C. §1350 adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 that:

(i) The accompanying Annual Report on Form 10-K for the year ended December 31, 2002 fully complies with the requirements of Section 13(a) or Section 15(d) of the Securities Exchange Act of 1934, as amended; and

(ii) The information contained in such report fairly presents, in all material respects, the financial condition and results of operations of Tellium, Inc.

/S/    HARRY J. CARR

Harry J. Carr

Chief Executive Officer