Ceramic-matrix composites of alumina and silicon carbide whiskers have recently found novel commercial application as electromagnetic absorbers. However, a detailed understanding of how materials issues influence the composite electrical response, which underpins this application, has been absent until now. In this project, such composites were electrically measured over a wide range of conditions and modeled in terms of various aspects of the microstructure in order to understand how they work. For this purpose, three types of composites were made by different methods from the same set of ceramic powder blends loaded with different volume fractions of whiskers. In doing so, the interfaces between whiskers, the preferred orientations of whiskers, and the structure of electrically-connected whisker clusters were varied; the whisker aspect-ratio distributions were the same for all methods. At the electrode interfaces, Schottky barriers at the junctions of the electrically-percolating wide-bandgap semiconductor whiskers on the surface were responsible for a significant portion of the total measured impedance. The associated electrical response was studied on the microscopic and macroscopic level, and the gap between these different scales was bridged. Also, a modeling approach was developed for the non-linear behavior of the composite which results from these barriers. In regards to the whiskers within the composite bulk, the effects of various factors on the wide-band frequency dependence of the dielectric response and dc conductivity were explained and contextualized for the electromagnetic absorber application. Such factors include whisker preferred orientation, electrical percolation and cluster structure, the interfaces between electrically-connected SiC whiskers, and porosity. A quantitative correlation between the anisotropy of the microstructure and that of the conductivity was found, and was understood in terms of the interfacial SiC-Al2O3-SiC conduction mechanism. This behavior was shown to differ from the behavior commonly observed for other disordered mixtures of relatively conductive particles dispersed inside insulating polymer hosts. A description of this new mechanism was developed based on an observed correlation between the temperature dependencies of the static and radio-frequency electrical responses. Also, the aforementioned non-linear response model was expanded upon to describe conduction through and across electrically-percolated clusters. The model demonstrates how loading and interface behavior influence the topology and the strength of the non-linear response of the clusters.