We prove a new rigorous upper bound on the vertical heat transport for Bénard-Marangoni  convection of a two-or three-dimensional fluid layer with infinite Prandtl number. Precisely, for Marangoni number the Nusselt number is bounded asymptotically by. Key to our proof are a background temperature field with a hyperbolic profile near the fluid's surface and new estimates for the coupling between temperature and vertical velocity.