This paper examines the differences and/or similarities between some of the commonly used canonical equations describing the effective permittivity and permeability of heterogeneous substrates with dielectric or metallic inclusions, at microwave frequencies. Graphical results are presented for the different structures considered. Simulated results from heterogeneous mixtures with both dielectric and metallic inclusions are presented, and compared with results from the canonical equation representation. Simulated results of a patch antenna on a heterogeneous medium and on its homogenous equivalent have also been presented.