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The effect of artificial magnetodielectric substrates on the impedance bandwidth properties of microstrip antennas is discussed. We review the results found in the literature and then focus on practically realizable artificial magnetic media operating in the microwave regime. Next, a realistic dispersive behavior of a practically realizable artificial substrate is embedded into the model. It is shown that frequency dispersion of the substrate plays a very important role in the impedance bandwidth characteristics of the loaded antenna. The impedance bandwidths of reduced size patch antennas loaded with dispersive magnetodielectric substrates and high-permittivity substrates are compared. It is shown that unlike substrates with dispersion-free permeability, practically realizable artificial substrates with dispersive magnetic permeability are not advantageous in antenna miniaturization. This conclusion is experimentally validated.