We analyze the matching and radiation properties of subwavelength resonant patch antennas filled with double-negative, double-positive, and/or single-negative metamaterial blocks. Analyzing the theoretical limits inherently present when loading such common radiators with metamaterials, we show how these configurations may exhibit in principle an arbitrarily low resonant frequency for a fixed dimension, but they may not necessarily radiate efficiently when their size is electrically small. However, interesting possibilities are suggested to overcome these limitations by employing circular or more complex patch geometries in order to select specific modes that, when appropriate loading ratios between the filling materials are chosen, also ensure radiation performance comparable qualitatively with a regular patch radiator of standard dimensions. Realistic numerical simulations, considering material dispersion, losses and the presence of the antenna feed are presented, showing how a practical realization is foreseeable. This may open novel venues in the design of small-scaled radiators with enhanced performance, which is of interest for many applications.