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A methodology is presented for the model order reduction of finite element approximations of passive electromagnetic structures characterized by statistical variability in material and geometry parameters. With such variability described in terms of an appropriate set of random variables, the proposed methodology offers a convenient and computationally-efficient framework for the development of a reduced order model using standard, deterministic model order reduction techniques. The generated stochastic reduced-order model lends itself to efficient quantitative assessment of the impact of statistical variability on the electromagnetic response of the component. Furthermore, the low order of the reduced model makes it suitable for use as a stochastic macromodel for the structure in the electromagnetic analysis of systems that include the structure under consideration as a component.