<Page>

                                                           Exhibit EX-99.906CERT

       Certification Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002
(Subsections (a) and (b) of Section 1350, Chapter 63 of Title 18, United States
Code)

In connection with the attached report of UBS Municipal Money Market Series (the
"Registrant") on Form N-CSR (the "Report"), each of the undersigned officers of
the Registrant does hereby certify that, to the best of such officer's
knowledge:

   1) the Report fully complies with the requirements of Section 13(a) or 15(d),
      as applicable, of the Securities Exchange Act of 1934, as amended;

   2) the information contained in the Report fairly presents, in all material
      respects, the financial condition and results of operations of the
      Registrant as of, and for, the periods presented in the Report.


Dated: September 5, 2003
       -----------------

By:   /s/ Joseph A. Varnas
      --------------------
      Joseph A. Varnas
      President


Dated:    September 5, 2003
          -----------------

By:   /s/ Paul H. Schubert
      --------------------
      Paul H. Schubert
      Treasurer

This certification is being furnished solely pursuant to 18 U.S.C. Section 1350
and is not being filed as part of the Report or as a separate disclosure
document.