Coplanar waveguide (CPW) has been finding wide applications in microwave integrated circuit (MIC) and monolithic microwave integrated circuit (MMIC) due to several advantages it offers over microstrip lines. Typical discontinuities characteristics are an integral part of practical circuit design. Therefore, a good understanding of their circuit behavior is essential for design success. In the past few decades, great effort has been made to accurate characterization of a variety of CPW circuits and discontinuities by developing different advanced fullwave approaches, of which the method of moments (MoM) has been considered as the most efficient and powerful algorithm. In this way, several commercial MoM simulators have been explored in the recent years for direct simulation and optimization of a large number of CPW circuit blocks with complicated configurations. However, such a direct approach requires the intensive CPU time and huge memory thus preventing one from physical insight into the operation principle of the whole CPW circuit block. Therefore, it is preferred to formulate the equivalent circuit models for many CPW elements such that the optimization can be executed via resultant network topology. The main goal of this thesis is to investigate various CPW discontinuities for CPWbased filter design and metamaterial characterization. To accomplish this task, the hybrid fullwave approach based on the method of moments (MoM) and short-open calibration (SOC) procedure, namely, MoM-SOC technique is firstly employed via two-port CPW discontinuity to extract equivalent circuit network parameters, i.e., Y-or