The idea of profile miniaturization and performance improvement of a rectangular patch antenna using a metamaterial substrate with large values in the real part of effective relative permeability is proposed in microwave frequency range. The volume profile of the antenna is minimized by tuning the effective relative permeability and thickness of the substrate material. The specific type of metamaterial which can be used as substrate material for the antenna miniaturization purpose is suggested. The proposed idea is validated through finite-difference time-domain (FDTD) simulations for sample rectangular patch antennas with metamaterial substrates at the frequency about 10 GHz. Improvement of the power directivity is found for the metamaterial substrate with large value in the real part of effective permeability. V C 2016 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:254-261, 2016.