An adaptive multi-element probabilistic collocation method to quantify uncertainties in electromagnetic compatibility and interference (EMC/EMI) analysis on electrically large, multi-scale, and complex platforms is presented. The method permits efficient and accurate statistical characterization of observables (i.e. quantities of interest such as coupled voltages), which vary rapidly and/or are discontinuous in random variables (i.e., parameterized quantities in system’s geometry, configuration, and excitation). The method achieves its efficiency and accuracy by recursively and adaptively dividing the random domain into sub-domains using as a guide the decay rate of relative error in the polynomial chaos expansion of the observables. While constructing local polynomial expansions at each sub-domain, a deterministic FFT-accelerated integral-equation-based hybrid (field-cable-circuit) simulator is used to compute the observable values at the collocation/integration points dictated by a proper integration rule. The adaptive multi-element probabilistic collocation method requires far less number of (computationally costly) deterministic simulations than the traditional collocation and Monte Carlo methods for computing the rapidly varying observables’ statistical moments and extracting their probability density functions. The efficiency and accuracy of the method are demonstrated via its applications to the statistical characterization of the voltages on shielded/unshielded microwave amplifiers as well as the magnetic fields induced on tire pressure sensors of cars.