We present a theory for reduced-order modelling of linear time-varying systems, together with efficient numerical methods for application to large systems. The technique, called TVP (Time-Varying Pad?), is applicable to deterministic as well as noise analysis of many types of communication subsystems, such as mixers and switched-capacitor filters, for which existing model reduction techniques cannot be used. TVP is therefore suitable for hierarchical verification of entire communication systems. We present practical applications in which TVP generates macromodels which are more than two orders of magnitude smaller, but still replicate the input-output behaviour of the original systems accurately. The size reduction results in a speedup of more than 500.