Identifying and understanding student difficulties with physics content in a wide variety of topical areas is an active research area within the physics education research community. Of particular value are investigations of physics topics that appear multiple times in different contexts across the undergraduate physics curriculum. As these common topics reappear, students' difficulties can perpetuate from one context to the next, or new difficulties can emerge as students encounter new physical contexts. One example of such a topic is boundary conditions, which is broadly considered to be an important topic that advanced physics undergraduates are expected to understand and apply in multiple topical areas including classical mechanics, quantum mechanics, and throughout electricity and magnetism. We report findings from an investigation of student difficulties using boundary conditions while focusing on the context of electromagnetic waves. Our data sources include student responses to traditional exam questions, conceptual survey questions, and think-aloud interviews. The analysis was guided by an analytical framework that characterizes how students activate, construct, execute, and reflect on boundary conditions during physics problem solving. Commonly observed student difficulties include activating boundary conditions in appropriate contexts, constructing a complex expression for the electromagnetic waves, mathematically simplifying and manipulating complex exponentials, and checking if the reflection and transmission coefficients are physical. We also present potential pedagogical implications based on our observations.