Traditional ontology alignment techniques enable equivalence relationships to be established between concepts in two ontologies with some confidence value. With semantic matching, however, it is possible to identify not only equivalence relationships between concepts, but less general and more general relationships. This is beneficial since more expressive relationships can be discovered between ontologies thus helping us to resolve heterogeneity between differing semantic representations at a finer level of granularity. This work concerns the application of semantic matching to the medical domain. We have extended the SMatch algorithm to function in the medical domain with the use of the UMLS metathesaurus as the background resource, hence removing its previous reliance on WordNet, which does not cover the medical domain in a satisfactory manner. We describe the steps required to extend the SMatch algorithm to the medical domain for use with UMLS. We test the accuracy of our approach on subsets of the FMA and MeSH ontologies, with both precision and recall showing the accuracy and coverage of different versions of our algorithm on each dataset.