Signal and power integrity design of interconnects, packages, and power delivery networks in the time domain requires equivalent circuit models which may only have characterizations available as tabulated admittance, impedance, or scattering parameters. Constructed numerical models with accurate fits to the measured or simulated data must satisfy causality, stability, and passivity conditions in order to preserve the physical characteristics of the original device. Several curve fitting algorithms are available to provide causal and stable model approximations with excellent fits to the data, however they can result in models with nonpassive behavior. In this thesis we investigate and demonstrate novel passivity enforcement algorithms based on sum-of-squares (SOS) polynomials for one-port and multiport networks using an existing causal and stable model. This is a convex problem; therefore, our methods provide globally optimum solutions. Our work grants fast solving time over standard globally optimum approaches and ensures passivity for all real frequencies. We provide several numerical examples using our algorithms to illustrate and compare the performance with other methods.