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Using numerical ray-tracing techniques, we study the propagation and absorption profiles of electromagnetic waves launched in the end cells of three different tandem mirrots: Phaedrus, an overdense low-temperature tandem mirror with plugs; TASKA, a conceptual tandem mirror with plugs and thermal barrier; and TMX-U, a tandem mirror with a significant hot-electron population. In particular, the effects of weakly relativistic thermal anisotropy on the absorption profile are examined. In general, at sufficiently low densities and temperatures, the X mode can access the plasma and achieve significant heating of the electrons. As the electron temperature increases, the X mode gets quickly absorbed at the edge and only the O mode achieves significant penetration and heating. For sufflciently large launching angles, the presence of thermal anisotropy can actually shift the region of maximum absorption towards the electron-cyclotron resonance layer. Regions of whistler instability appear along rays launched nearly along the machine axis, when the thermal-anisotropy ratio, temperature, and density reach sufficiently high values.