We discuss computationally efficient ways of accounting for the impact of uncertainty, e. g., lack of detailed knowledge about sources, materials, shapes, etc., in computational time-domain electromagnetics. In contrast to classic statistical Monte Carlo-based methods, we explore a probabilistic approach based on high-order accurate expansions of general stochastic processes. We show this to be highly efficient and accurate on both one- and two-dimensional examples, enabling the computation of global sensitivities of measures of interest, e. g., radar-cross-sections (RCS) in scattering applications, for a variety of types of uncertainties.