This paper describes a rigorous numerical approach for characterizing coplanar waveguide (CPW) discontinuities. This approach develops an integral equation for the unknown electric field distribution on the slot apertures and then solves it numerically in the space domain using the method of moments (SDIE). As a demonstration, this method is applied to derive frequency dependent equivalent circuits for the case of a short-end slotline, a short- and an open-end CPW. In addition, the S-parameters of a CPW stub are computed as a demonstration of a two port discontinuity. It is shown that a shorted slotline and a shorted coplanar waveguide always behave as inductive loads. However, in the case of an open-end coplanar waveguide the even and odd excitations create different effects. Specifically, the even excitation corresponds to an inductive load while the odd excitation to a capacitive one. The results derived by the SDIE method have been extensively studied for numerical convergence and have been compared to other available theoretical or experimental data. The agreement is very good.