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The purpose of this review paper is to critically examine some the physics-based fundamental limitations. Using metamaterials and/or other exotic physical phenomena for performance. This, in turn, prompts us to critically examine the effective medium theories, and rigorously model the physical structures that show promise rather than their effective medium equivalents to see if indeed their actual performance is consistent with that predicted by their effective medium representation. The paper investigates several representative structures, such as substrates and superstrates for microstrip patch antennas, to sort out the issue mentioned above, and concludes that the only reliable approach to characterizing these media is to simulate the physical structure, and not rely solely on their effective medium representations. Next, the paper develops a systematic strategy to designing antenna/meta-material composites that totally bypasses the effective medium approach.