Method of line (MOL) procedure is very useful in the analysis of radiative and transmissive microwave components, but its standard version does not allow for the study of elements with complex substrates. In this work, we first show that components integrated into materials exhibiting the magneto-electric effect (biisotropic and general bianisotropic media) cannot be analyzed following a standard MoL algorithm. Next, we derive an extended MoL numerical tool, which allows for the analysis of components in the presence of any linear medium (even inhomogeneous, bianisotropic and lossy). Such an extension is based on the generalization of the transmission.line equations for a general linear medium, which, in the case in point, are not necessarily decoupled. Furthermore, we present the full coincidence of this new method with the standard MoL in the case of simpler media (i.e., not exhibiting the magneto-electric effect) and, finally, we show some numerical results, obtained analyzing microwave antennas and resonators with bianisotropic and chiral substrates. [ABSTRACT FROM AUTHOR]