Microstrip patch antennas have problems of low bandwidths. The aim of this chapter is to show various ways to overcome this problem by using various matching techniques for numerous patch antenna array schemes. Various approaches are used for estimating the figures of merit such as VWSR and the S11 parameter of such antennas. These patch antenna performance characteristics are addressed by simulation techniques using the full-wave method of moments (MoM). Patch antennas are also modelled as a reduced model, in an effective homogeneous dielectric space, to reduced the simulation time. Lastly a more efficient reduced model using special planar Green's functions with and without the use of non radiating networks are explained qualitatively.