This work described in this book develops a computationally efficient approach to performing electromagnetic simulations in the presence of statistically defined uncertainties caused by either material inhomogeneities or fabrication and placement tolerances. Comparisons are made with results from Monte Carlo simulations and a sequence of higher order approximation extensions is considered. There are two main statistical techniques used to achieve the overall objective of this book namely: the Direct Solution Technique (DST) and the Unscented Transform (UT) method. The case studies used are developed using the Transmission Line Modelling (TLM) method.