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Electromagnetic heating is the process where a composite material absorbs applied electromagnetic radiation and converts this energy to internal energy in the material. While homogenization models for electromagnetic heating have been around for decades, these approaches break down when the wavelength of the electromagnetic wave is comparable to the characteristic microscale length. Here we derive from Maxwell's equations and the energy equation effective equations for a binary composite in the case where the characteristic microscale length and wavelength are compa- rable. Under the assumption of small loss factors in the materials, high-frequency homogenization results in a locally temperature dependent elliptic problem for the field amplitude via Floquet--Bloch theory. The length scale for thermal transport is the macroscale, and classical homogenization applies. We characterize the results in terms of a complex wavenumber for propagation, and validate our results for a lamellar structure for which an exact solution exists under isothermal conditions, and characterize field strength needed to achieve thermal runaway in the composite as a function of the resonant frequency and volume fraction of the lossless material. [ABSTRACT FROM AUTHOR]