Five types of nanofillers, namely, silica, surface-silylated silica, alumina, surface-silylated alumina, and boron nitride, were tested in this study. Nanocomposites composed of an epoxy/amine resin and one of the five types of nanoparticles were tested as dielectrics with a focus on (i) the surface functionalization of the nanoparticles and (ii) the water absorption by the materials. The dispersability of the nanoparticles in the resin correlated with the composition (OH content) of their surfaces. The interfacial polarization of the thoroughly dried samples was found to increase at lowered frequencies and increased temperatures. The β relaxation, unlike the interfacial polarization, was not significantly increased at elevated temperatures (below the glass-transition temperature). Upon the absorption of water under ambient conditions, the interfacial polarization increased significantly, and the insulating properties decreased or even deteriorated. This effect was most pronounced in the nanocomposite containing silica, and occurred as well in the nanocomposites containing silylated silica or non-functionalized alumina. The alternating current (AC) breakdown strength of all specimens was in the range of 30 to 35 kV·mm−1. In direct current (DC) breakdown tests, the epoxy resin exhibited the lowest strength of 110 kV·mm−1; the nanocomposite containing surface-silylated alumina had a strength of 170 kV·mm−1. In summary, water absorption had the most relevant impact on the dielectric properties of nanocomposites containing nanoparticles, the surfaces of which interacted with the water molecules. Nanocomposites containing silylated alumina particles or boron nitride showed the best dielectric properties in this study.