A central problem in undergraduate mathematics education for future engineers consists in the perceived and actual relevance of the mathematical content. One strategy to strengthen both is to let students experience how that content appears in posing and solving authentic problems from the field of engineering which the students have signed up to study. This paper proposes a way to develop such a strategy, both in terms of theoretical precision (e.g. to clarify what "authentic" could mean in this context), and in terms of the institutional and epistemological conditions and constraints for realizing the strategy. The paper is based on cases and formats developed over twenty years at the Technical University of Denmark.