The shock termination of a relativistic magnetohydrodynamic wind from a pulsar is the most interesting and viable model for the excitation of the synchrotron sources observed in plerionic supernova remnants. We have studied the structure of relativistic magnetosonic shock waves in plasmas composed purely of electrons and positrons, as well as those whose composition includes heavy ions as a minority constituent by number. We find that relativistic shocks in symmetric pair plasmas create fully thermalized distributions of particles and fields downstream. Therefore, such shocks are not good candidates for the mechanism which converts rotational energy lost from a pulsar into the nonthermal synchrotron emission observed in plerions. However, when the upstream wind contains heavy ions which are a minority constituent by number density, but carry the bulk of the energy density, much of the energy of the shock goes into a downstream, nonthermal power-law distribution of positrons with energy distribution N(E)dE ∝ E–s. In a specific model presented in some detail, s = 3. These characteristics are close to those assumed for the pairs in macroscopic MHD wind models of plerion excitation. The essential mechanism is collective synchrotron emission of left-handed extraordinary modes by the ions in the shock front at high harmonics of the ion-cyclotron frequency, with the downstream positrons preferentially absorbing almost all of this radiation, mostly at their fundamental (relativistic) cyclotron frequencies. Possible applications to the models of plerions and to constraints on theories of energy loss from pulsars are briefly outlined.