Exhibit 99.906CERT

Certification Pursuant to 18 U.S.C. 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002; provided by the Chief Executive Officer and Chief Financial Officer, based on each such officer’s knowledge and belief.

The undersigned officers of Nuveen Select Tax-Free Income Portfolio 3 (the “Fund”) certify that, to the best of each such officer’s knowledge and belief:

1.   The Form N-CSR of the Fund for the period ended March 31, 2021 (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 Fund.

Date: June 4, 2021

/s/ David J. Lamb

David J. Lamb

Chief Administrative Officer

(principal executive officer)

/s/ E. Scott Wickerham

E. Scott Wickerham

Vice President, Controller

(principal financial officer)