In a system of dielectric matrix–conducting particles, the dielectric characteristics are analyzed over a wide frequency range (3–37 GHz). Experimental values of the dielectric constant e′ and dielectric loss tangent tanδ are presented for pressureless sintered AlN-based composites with different contents of the conducting particles (Mo, W, and TiN) within the interval from 0% to the percolation threshold. Both the real e′ and imaginary e″ parts of the dielectric constant of the investigated composites monotonically increased, reaching maximum values (e′ = 15 – 26.5, e″ = 0.14–0.28) when the content of the conductive particles approached the percolation threshold. The dielectric loss tangent of the composites, depending on the conducting particle content, reached values of 0.0085 for AlN–16.6%Mo, 0.0095 for AlN–16%W, and 0.0105 for AlN–20.4%TiN. The dielectric losses e″ in the AlN-based composites, as long as they remain nonconductive for the direct current, are low compared to losses of e″ = 0.04 in polycrystalline AlN ceramics and exceed them by only 4–7 times. A relationship between the dielectric losses and the level of microwave absorption has been established. The dielectric characteristics, electrical resistance, and thermal conductivity of the produced AlN-based composites and their achievement of a high absorption of the microwave radiation (L = 23–32 dB/cm) make these materials promising bulk absorbers in microwave devices (TWTs, klystrons).