Fresnel equations predict that an ultrathin free standing conductive ﬁlm, thousands times thinner than skin depth, is capable to absorb up to 50% of incident electromagnetic radiations. In the microwave range, the same holds true for a free standing graphene sheet. We demonstrate theoretically and prove experimentally that microwave absorptance of graphene can be enhanced considerably by depositing graphene on a dielectric substrate. On the experimental side, we obtain 80% and 65% absorptance at 30GHz and 1 THz, respectively. Theory predicts that higher absorptance can be achieved with a suitable choice of the dielectric permittivity and the thickness of the substrate. Absorption can also be maximized by choosing the optimum incidence angle for s-polarized waves in free space or by working in the vicinity of the cut-off frequency of the transverse electric mode in waveguide conﬁguration. The polarization sensitivity of the transmittance and reﬂectance of graphene layers can be used to tune the polarization state of the transmitted and reﬂected radiations.