A generalised formulation of the moment matching problem, which encompasses previous formulations and is applicable to non-square continuous and discrete systems, is presented. The formulation entails points about which moments can be matched. These points can be specified either by trial and error or by means of optimisation, so that the reduced model has desirable properties such as stability and accuracy. Novel properties of Pade approximants for non-square systems are elucidated, and details of the approach are illustrated by means of examples.