This study investigates the effect of nanodiamond and nanographite fillers on the dielectric properties of epoxy resin composites. Cylindrical specimens based on epoxy resin EPICOTE 828 with an anhydride curing agent were fabricated in neat form and with the addition of 0.6 wt.% nanodiamonds or nanographite. The dielectric response was measured using a resonant Q-meter method in the frequency range of 0.1–100 kHz. The developed experimental setup, combining the Q-meter with a digital voltmeter and a frequency counter, enabled reliable determination of dielectric permittivity and dielectric loss tangent. The results demonstrate that the incorporation of nanodiamonds reduces the dielectric permittivity compared with the neat epoxy binder. This decrease indicates a reduction in the number of polar groups and an increase in the structural ordering of the polymer matrix. In contrast, the addition of nanographite leads to a slight increase in dielectric permittivity, which suggests the formation of additional polarization pathways and a more disordered polymer structure. The scientific novelty of the study lies in providing a comparative analysis of nanodiamond and nanographite fillers in epoxy composites using resonant dielectric spectroscopy. The findings highlight the different mechanisms by which carbon-based nanofillers alter the dielectric behavior of polymers, offering practical guidance for tailoring epoxy-based composites for electrical insulation and related engineering applications.