In order to evaluate ontology matching algorithms it is necessary to confront them with test ontologies and to compare the results with some reference. The most prominent comparison criteria are precision and recall originating from information retrieval. Precision and recall are thought of as some degree of correction and completeness of results. However, when the objects to compare are semantically defined, like ontologies and alignments, it can happen that a fully correct alignment has low precision. This is due to the restricted set-theoretic foundation of these measures. Drawing on previous syntactic generalizations of precision and recall, semantically justified measures that satisfy maximal precision and maximal recall for correct and complete alignments is proposed. These new measures are compatible with classical precision and recall and can be computed.