The results of mode-matching is generally not analytic. For example, consider a waveguide step junction, you can analyze it by expressing the fields on two side of the junction in terms of a large number of modes. You would get the coupling coefficients (numerical) between those modes. If you take only one or two on each sides, you might get some analytical formula. But that is valid under restricting conditions.
For simple discontinuity, many people have worked out analytical formula for the elements for an equivalent circuits. If it is available, (I think) it should have been built into a circuit modeler. Check ADS for for the components of your interest