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Simulations of coupled circuit-electromagnetic systems require heavy time-stepping computations often involving several thousand time-varying variables in the finite element (FE) models. However, in most cases, the actual dynamics of interest are between only a few of the variables, for which model reduction strategies based on Krylov subspace projection provide a promising alternative. They often drastically reduce computation time while reproducing practically the same dynamics between the variables of interest. Moreover, the time-evolution of the many other variables can also be recovered easily whenever required with reasonable accuracy. Based on this, a modeling and simulation strategy is presented for coupled field-circuit systems, involving a two-stage model reduction process. It significantly extends an earlier reported approach. Numerical results are presented for a generic field-circuit system with promising results, illustrating the performance of the strategy compared to conventional FE time-step computations.