Electron cyclotron resonance frequency wave and absorption theory and ray tracing are reviewed and a numerical model for the study of electron heating in tandem mirror plugs and barriers is presented. It is found that substantial shifts in the spatial energy deposition profile occur from the cold plasma electron cyclotron resonance at elevated temperatures and that surface absorption can be substantial. The O-mode exhibits a ray trajectory that more easily penetrates to the plasma core and has an adequate single-pass absorption at temperatures > 10 keV.