Theoretical equivalence and duality are two closely related notions: but their interconnection has so far not been well understood. In this paper I explicate the contribution of a recent schema for duality to discussions of theoretical equivalence. I argue that duality suggests a construal of theoretical equivalence in the physical sciences. The construal is in terms of the isomorphism of models, as defined by the Schema. This construal entails interpretative constraints that should be useful for theoretical equivalence more generally. I illustrate the construal in various formulations of Maxwell's electromagnetic theory.