Variational expressions for the capacitances of asymmetrical and coupled coplanar-type transmission lines are derived. These expressions are quite general and are applicable to a wide class of coplanar-type transmission lines, including those containing an anisotropic media. These expressions are used in conjunction with an accurate and efficient numerical method based on the Ritz procedure. Numerical results are shown for the line characteristics of asymmetrical and coupled coplanar-type lines with anisotropic media and are compared with the exact analytical solutions for the special case of air as the substrate material. The comparison is found to be quite favorable.