The rf magnetoresistance of Fe/Cr superlattices is studied for two orientations of the current: parallel and across the superlattice layers. A mutually single-valued correspondence is established between the relative magnetoresistance measured at dc current and the change in the transmission coefficient of electromagnetic waves in the magnetic field. When rf currents flow across the layers, the relative change in the signal amplitude is proportional to twice the change in the electrical resistance of the superlattice and is of opposite sign. It is shown that the rf losses are determined by the surface resistance which is proportional to the superlattice thickness and inversely proportional to its conductivity. An equation is derived for the rf electric field distribution in the superlattice. It is established that when the thickness of the superlattice is small compared with the skin layer depth, field and current components which penetrate through the entire superlattice exist.