Exhibit 32(b)

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 TII Network Technologies, Inc. (the “Company”) on Form 10-Q for the quarter ended December 31, 2004, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Kenneth A. Paladino, Principal Financial Officer 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.

Date: February 11, 2005

                         /s/Kenneth A. Paladino                      
Kenneth A. Paladino
       (Principal Financial Officer)