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 Annual Report on Form 10-K for the period ending December 31, 2011, of Tennessee Gas Pipeline Company, L.L.C. (the “Company”) as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, John R. Sult, Executive Vice President and Chief Financial Officer, certify (i) that the Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended, and (ii) that the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

A signed original of this written statement required by Section 906 has been provided to Tennessee Gas Pipeline Company, L.L.C. and will be retained by Tennessee Gas Pipeline Company, L.L.C. and furnished to the Securities and Exchange Commission or its staff upon request.