Efficient cosmic-ray production can have a significant effect on the evolution and X-ray emission from SNRs. Using hydrodynamic simulations coupled to diffusive shock acceleration, we produce thermal and nonthermal forward-shock photon spectra. For a given ambient density and explosion energy, we find that the position of the forward shock at a given age is a strong function of the acceleration efficiency, providing a signature of cosmic-ray production. Using an approximate treatment for the ionization state of the plasma, we investigate the effects of slow versus rapid heating of the postshock electrons on the ratio of thermal to nonthermal X-ray emission at the forward shock. We also investigate the effects of magnetic field strength on the observed spectrum for efficient cosmic-ray acceleration. The primary effect of a large field is a flattening of the nonthermal spectrum in the soft X-ray band. X-ray spectral index measurements may thus be indicators of the postshock magnetic field strength. The predicted gamma-ray flux from inverse Compton (IC) scattering and neutral pion decay is strongly affected by the ambient conditions, and for the parameters used in our examples, the IC emission at E ~ 1 TeV exceeds that from pion decay, although at both lower and higher energies this trend is reversed for cases of high ambient density. More importantly, high magnetic fields produce a steepening of the electron spectrum over a wide energy range, which may make it more difficult to differentiate between IC and pion-decay emission solely by spectral shape.