Insulating materials filled with conducting particles permit tailoring of electrical, electromagnetic and thermal properties of the resulting composite. When the filler particles are small and metallic, a dielectric relaxation due to interfacial polarization is commonly observed at optical or smaller wavelengths. Here, experimental results are presented in which the dielectric relaxation is shifted to microwave frequencies as a result of using metal-coated dielectric particles with a nano-scale coating thickness. The results are analysed in the context of effective medium theory adapted for multi-layer particles. Such a large shift in relaxation frequency, compared with that for a similar composite with solid metal filler particles, is shown to be a function of both the coating geometry and a thin-film-related reduction in the conductivity of the metal. The observed broadening of the relaxation peak is attributed to non-uniformity of the coating thickness and a consequent distribution of coating conductivity.