Recent theoretical studies have shown that circular patch antennas loaded by an inhomogeneous substrate partially filled with a mu-negative (MNG) metamaterial may in principle support a resonant radiating mode, even if the total size of the radiator is significantly smaller than the wavelength of operation. In those theoretical analyses, MNG metamaterials have been assumed as continuous, isotropic and readily available materials, characterized by a proper dispersion in frequency and by inherent ohmic losses. The fabrication of such compact antennas, however, would require the major effort of designing proper subwavelength inclusions that realize the MNG behavior of the substrate, and consequently a careful design of their geometry, location and orientation. The fabrication of a fully isotropic MNG sample to reside underneath the sub-wavelength patch, moreover, may be challenging with the current technological limitations. In this paper, we first show that the proposed sub-wavelength radiator may operate even when the fabricated MNG sample is not isotropic, due to the specific polarization of the magnetic field in the MNG region. Then, we propose a complete design of the magnetic inclusions, presenting full-wave numerical simulations of the structure, which effectively supports the expected resonant mode, despite the small size of the antenna. The comparisons among analytical results of the patch loaded by: (a) the ideal MNG sample applying a simple cavity model; (b) full-wave numerical simulations of the same antenna considering the presence of the feed; and (c) full-wave numerical simulations of the antenna loaded by the proposed magnetic inclusions, show how our design effectively simulate the presence of an MNG sample, allowing the realistic design of a sub-wavelength metamaterial patch antenna with satisfactory matching and radiating features. This may open up new venues in the realization of efficient metamaterial radiating components for practical purposes.