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In this paper, we generalize a recently proposed method for model reduction of linear systems to the frequencyweighted case. The method uses convex optimization and can be used both with sample data and exact models. We also derive simple a priori bounds on the frequency-weighted error. We combine the method with a rank-minimization heuristic, to approximate multi-input–multi-output systems. We also present two applications — environment compensation and simpli�cation of interconnected models — where we argue the proposed methods are useful.