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In recent years, order-reduction techniques based on Krylov subspaces have become the methods of choice for generating macromodels of large multi-port RLC circuits. A widely-used method of this type is PRIMA. Its main features are provably passive reduced-order models and a moment-matching property. On the other hand, PRIMA does not preserve other structures, such as reciprocity or the block structure of the circuit matrices, inherent to RLC circuits, which makes it harder to synthesize the PRIMA models as actual circuits. Moreover, the PRIMA models match only half as many moments as optimal, but non-passive, moment-matching techniques such as SyMPVL. In this paper, we propose the reduction technique SPRIM that overcomes these disadvantages of PRIMA. In particular, SPRIM generates provably passive and reciprocal macromodels of multi-port RLC circuits, and the SPRIM models match twice as many moments as the corresponding PRIMA models obtained with identical computational work. Numerical results are reported that illustrate the higher accuracy of SPRIM vs. PRIMA.