A fast stochastic collocation method for statistically characterizing electromagnetic interference and compatibility (EMI/EMC) phenomena on electrically large and loaded platforms is presented. Uncertainties in electromagnetic excitations and/or system geometries and configurations are parameterized in terms of random variables having normal or beta probability density functions. A fast time-domain integral-equation-based field-cable-circuit simulator is used to perform deterministic EMI/EMC simulations for excitations and/or system geometries and configurations specified by Stroud integration rules. Outputs of se simulations then are processed to compute averages and standard deviations of pertinent observables. The proposed Stroud-based collocation method requires far fewer deterministic simulations than Monte Carlo or tensor-product integrators. To demonstrate the accuracy, efficiency, and practicality of the proposed method, it is used to statistically characterize coupled voltages at the feed pins of cable-interconnected and shielded computer cards as well as the terminals of cables situated inside the bay of an airplane cockpit.