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Model-order reduction techniques of RF and microwave linear and weakly nonlinear time-varying circuits are presented. The reduced models capture the memory and linear or weakly nonlinear input-output behavior of the circuit, as well as the matching conditions at the model ports. The reported techniques serve to reduce models of a number of RF and microwave functions such as lumped or distributed linear circuits, small-signal amplifiers, mixers, modulators, etc. The reduced models can be implemented in any simulator using standard library components and can be employed both in frequency and time-domain simulations, demonstrating good agreement and significant reduction of simulation time with respect to the simulation of the complete circuit. The model-order reduction techniques are illustrated through different examples.