An increasing interest is arising in developing miniaturized antennas in the microwave range. However, even when the adopted antennas dimensions are small compared with the wavelength, radiation performances have to be preserved to keep the system-operating conditions. For this purpose, magneto-dielectric materials are currently exploited as promising substrates, which allows us to reduce antenna dimensions by exploiting both relative permittivity and permeability. In this paper, we address generic antennas in resonant conditions and we develop a general theoretical approach, not based on simplified equivalent models, to establish topologies most suitable for exploiting high permeability and/or high-permittivity substrates, for miniaturization purposes. A novel definition of the region pertaining to the antenna near-field and of the associated field strength is proposed. It is then showed that radiation efficiency and bandwidth can be preserved only by a selected combinations of antenna topologies and substrate characteristics. Indeed, by the proposed independent approach, we confirm that non-dispersive magneto-dielectric materials with relative permeability greater than unit, can be efficiently adopted only by antennas that are mainly represented by equivalent magnetic sources. Conversely, if equivalent electric sources are involved, the antenna performances are significantly degraded. The theoretical results are validated by full-wave numerical simulations of reference topologies.