The geometry and structure of an interface ultimately determines the behavior of devices at the nanoscale. We present a generic method to determine the possible lattice matches between two arbitrary surfaces and to calculate the strain of the corresponding matched interface. We apply this method to explore two relevant classes of interfaces for which accurate structural measurements of the interface are available: (i) the interface between pentacene crystals and the (1 1 1) surface of gold, and (ii) the interface between the semiconductor indium-arsenide and aluminum. For both systems, we demonstrate that the presented method predicts interface geometries in good agreement with those measured experimentally, which present nontrivial matching characteristics and would be difficult to guess without relying on automated structure-searching methods.