A variety of models have been explored in regard to the origin of the excess extreme-ultraviolet (∼0.1 keV) emission in the Coma cluster. It is now established that the flux is nonthermal, and the only nonthermal source mechanism that appears viable is inverse Compton emission produced by ∼100 MeV electrons interacting with the cosmic microwave background photons. All but one of the models that have been proposed require a cluster magnetic field less than 1 μG. However, recent observations strongly suggest that the magnetic field in the Coma cluster is ∼5 μG. We investigate the constraints on models imposed by a 5 μG cluster field and find a limited class of models that are compatible with this constraint. We also investigate the possibility that the excess hard (40-60 keV) X-ray emission in the cluster is produced by inverse Compton emission with the same electron population that produces the EUV excess. We find no scenarios that are compatible with a large cluster magnetic field, and consequently, in this case, these two components must be unrelated.