The study of (generally weak) relativistic damping of waves in plasmas is not new, but the principal analytical results have been obtained through a series of approximations leading to expressions for the dielectric tensor elements in terms of weakly relativistic plasma dispersion functions, where μ = mec2/kTe≫1. If one focuses only on the case with propagation perpendicular to the magnetic field, however, where there is no damping at all without relativistic effects, it is possible to reduce the exact calculation of each dielectric tensor element to one or two integrals without sums or approximation. The exact results are compared with two approximate methods that do not involve a numerical integration, one being the weakly relativistic appproximation and the other a new extension to moderately relativistic plasmas.