This article describes a curricular innovation designed to help students experience authentic physics inquiry with an emphasis on computational modeling and scientific communication. The educational design centers on a new type of assignment called a computational essay, which was developed and implemented over the course of two semesters of an intermediate electricity and magnetism course at the University of Oslo, Norway. We describe the motivation, learning goals, and scaffolds used in the computational essay project, with the intention that other educators will be able to replicate and adapt our design. We also report on initial findings from this implementation, including key features of student-written computational essays, student reflections on the inquiry process, and self-reported conceptual and attitudinal development. Based on these findings, we argue that computational essays can serve a key role in introducing students to open-ended, inquiry-based work and setting the foundation for future computational research and studies.