There is an increasing interest in developing miniaturized antennas for ultra-low power applications (tens of μW) in the microwave range. However, to guarantee the system operations in such low-power conditions, radiation performances need to be preserved even if the adopted antennas dimensions are small compared to the wavelength. For this purpose, magneto-dielectric materials are currently exploited as promising substrates. In this paper we demonstrate by a theoretical approach that radiation efficiency can be preserved only by selected combinations of antenna topologies and substrate characteristics. Indeed, materials with relative permeability greater than unit, can be efficiently adopted only by antennas that may be represented as equivalent magnetic sources. Conversely, we demonstrate that if equivalent electric sources are involved, the antenna performance are significantly degraded. The analytical development is then confirmed by full-wave numerical simulations.