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In this paper, we present a methodology for generating guaranteed passive time-domain models of subsystems described by tabulated frequency-domain data obtained through measurement or through physical simulation. Such descriptions are commonly used to represent on- and off-chip interconnect effects, package parasitics, and passive devices common in high-frequency integrated circuit applications. The approach, which incorporates passivity constraints via convex optimization algorithms, is guaranteed to produce a passive-system model that is optimal in the sense of having minimum error in the frequency band of interest over all models with a prescribed set of system poles. We demonstrate that this algorithm is computationally practical for generating accurate high-order models of data sets representing realistic, complicated multiinput, multioutput systems.