Congruence with respect to process algebraic operators is an important characteristic for a behavioural semantics. A widely used method to ensure this property is to single out a semantics, and impose syntactic restrictions on the structural operational semantics definition of operators. In this study, we approach this issue from the operator’s point of view. Given an operator, we find constraints on the modal characterization of semantics to guarantee that the semantics is a congruence with respect to that operator. We extend previous results regarding concrete semantics to include the renaming operator, and extend this work to weak semantics.