Novel design of a dual band microstrip circular patch antenna loaded with ENG ( εnegative) metamaterial has been shown in the first section. Using ENG metamaterial instead of the conventional dielectric, unconventional TM δ10 ( ) mode was produced to yield a dual band performance. Optimized parameters such as permittivity ( ε 1) and filling ratio ( ) of metamaterials were selected with the aid of a MATLAB based parameter optimization algorithm, developed for all these sort of patch antennas. In the second section, a dual band circular patch antenna loaded with MNG (µ negative) metamaterial has been reported. An unconventional modified TM δ10 ( ) mode has been produced along with conventional TM 110mode due to using MNG metamaterial. Here also the optimum values of permeability (µ 1) and filling ratio ( ) for these sorts of patch antennas have been calculated from a MATLAB based parameter optimization algorithm. Both the proposed antennas provide good and resonance and satisfactory radiation performances (directivity, radiation efficiency, and gain) with a dual band performance.