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In this paper, the unique features of periodic magneto-dielectric meta-materials in electromagnetics are addressed. These materials, which are arranged in periodic configurations, are applied for the design of novel EM structures with applications in the VHF-UHF bands. The utility of these materials is demonstrated by considering two challenging problems, namely, design of miniaturized electromagnetic band-gap (EBG) structures and antennas in the VHF-UHF bands. A woodpile EBG made up of magneto-dielectric material is proposed. It is shown that the magneto-dielectric woodpile not only exhibits band-gap rejection values much higher than the ordinary dielectric woodpile, but also for the same physical dimensions it shows a rejection band at a much lower frequency. The higher rejection is a result of higher effective impedance contrasts between consecutive layers of the magneto-dielectric woodpile structure. Composite magneto-dielectrics are also shown to provide certain advantages when used as substrates for planar antennas. These substrates are used to miniaturize antennas while maintaining a relatively high bandwidth and efficiency. An artificial anisotropic meta-substrate having μr>εr, made up of layered magneto-dielectric and dielectric materials is designed to maximize the bandwidth of a miniaturized patch antenna. Analytical and numerical approaches, based on the anisotropic effective medium theory (AEMT) and the finite-difference time-domain (FDTD) technique, are applied to carry out the analyzes and fully characterize the performance of finite and infinite periodic magneto-dielectric meta-materials integrated into the EBG and antenna designs.