Most intriguing and complicated scientific problems are solved with the aid of high-speed computers. Advancements in computer technology in conjunction with lower cost of computers have tremendously contributed to this effort. In this thesis, adopting the same philosophy, we explore the solutions to electromagnetic problems using a numerical technique, namely the Finite Difference Time Domain technique. This technique requires large computer resources: specifically, fast computing and large amount of computer memory. Therefore, our developments of this numerical technique focus on reducing both the computational time and computer memory requirements. A unique line-of-sight (LoS) approximation to the equivalence principle, which is a far more efficient alternative to the standard equivalence principle, is introduced. This includes the theory associated with the LoS equivalence, the examination of the error due to the approximation, and the verification with simulations and measurements. The FDTD method is formulated by discretizing Maxwell's curl equations over a finite volume and approximating the derivatives with central difference approximations. The error due to this approximation depends directly on the method of implementation such as the non-uniform mesh. An experimental investigation of the numerical error due to the non-uniform FDTD technique is presented. In the area of active and passive microwave devices, a unique method of incorporating the device equations into the FDTD algorithm is presented. The measurement and simulation results verify this method. In addition to device analysis, new antennas for the use in Personal Communication Systems are presented. The finale to the thesis is an electromagnetic simulation software package that incorporates all the new techniques developed in the course of this work.