In this work we study the ac dissipation of mesoscopic superconductors at microwave frequencies using the time dependent Ginzburg-Landau equations. Our numerical simulations show that the ac dissipation is strongly dependent on the orientation of the ac magnetic field (h(ac)) relative to the dc magnetic field (H-dc). When h(ac) is parallel to H-dc we observe that each vortex penetration event produces a significant suppression of the ac losses because the imaginary part of the ac susceptibility as a function of H-dc increases before the penetration of vortices, and then it decreases abruptly after vortices have entered into the sample. In the second case, when h(ac) is perpendicular to H-dc, we observe that the jumps in dissipation occur at the same values of H-dc but are much smaller than in the parallel configuration. The behavior of the dissipation in the perpendicular configuration is similar to previous results obtained in recent microwave experiments using mesoscopic lithographed squares of Pb [A.D. Hernandez, O. Ares, C. Hart, D. Dominguez, H. Pastoriza, A. Butera, J. Low Temp. Phys. 135 (2004) 119]. (C) 2007 Elsevier B.V. All rights reserved.