A method for the description of the fields in finlines on anisotropic substrates is presented. The method also allows the complex tensor character of all material parameters and the influence of second-order effects, such as metallisation thickness, to be taken into account. The principal boundary value problem can be described with the help of a relatively small eigenmatrix and so the numerical treatment demands little work. Numerical and measurement results are presented, and discussed, for the transmission properties and for the field and power distributions. Furthermore, a suitable definition of the characteristic impedance is introduced, having in mind CAD applications. Design procedure and measurement characteristics for nonreciprocal elements are also included.