Field-theoretical equivalent circuit models of a variety of coplanar waveguide (CPW) lumped-element discontinuities for two dominant modes are characterized by executing the short-open calibration (SOC) procedure in the fullwave method of moments (MoM). In our developed MoM platform, the impressed current sources with even or odd symmetry are introduced at the selected ports in order to separately excite the even and odd dominant modes, i.e., CPW- and CSL-mode. After the port network parameters are numerically derived using the Galerkin's technique, the two SOC standards are defined and evaluated in the self-consistent MoM to effectively de-embed and extract the core model parameters of a CPW circuit or discontinuity. After the validation is confirmed via comparison with the published data, extensive investigation is carried out to for the first time demonstrate the distinctive model properties of one-port CPW short- and open-end elements as well as two-port inductive and capacitive coupling elements with resorting to its two different dominant modes.