Radiation of dileptons and photons from high-energy nuclear collisions provides information on the space-time evolution of the hot dense matter produced therein. We compute this radiation using relativistic hydrodynamics and a coarse-grained version of the microscopic event generator UrQMD, both of which provide a good description of the hadron spectra. The currently most accurate dilepton and photon emission rates from perturbative QCD and from experimentally based hadronic calculations are used. Comparisons are made to data on central Pb-Pb and Pb-Au collisions taken at the CERN SPS at a beam energy of 158A GeV. Both hydrodynamics and UrQMD provide very good descriptions of the photon transverse momentum spectrum measured between 1 and 4 GeV. but slightly underestimate the low-mass spectrum of e+ e- pairs, even with greatly broadened ρ and ω vector mesons. Predictions are given for the transverse momentum distribution of dileptons.