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Following our recent findings on the possibility of squeezing the resonant dimensions of circular patch antennas by using negative-permeability loadings, here we theoretically and numerically analyze sub-wavelength elliptical patch antennas partially loaded with magnetic metamaterials. First, we formulate a general theory for inhomogeneously loaded subwavelength elliptical patch antennas, deriving a closed-form solution for the modes supported by this geometry in the long wavelength limit. Our theory proves that their resonant size may be in principle squeezed to any arbitrarily small dimension, provided that the properties of the loading metamaterial are properly tailored. Then, we highlight several advantages offered by the elliptical shape: two orthogonal modes may be independently excited within a subwavelength volume, providing large flexibility in the design, and more degrees of freedom compared to the circular geometry. In particular, the odd mode is shown to provide better gain than the circular case, due to larger aperture efficiency. Full-wave simulations, considering a finite ground plane, realistic feed and the influence of metamaterial loss, prove that the elliptical geometry presents great potentials for a variety of electrically small low-profile antenna applications.