The issues influencing student engagement with high-stakes computer-based exams were investigated, drawing on feedback from two cohorts of international MA Education students encountering this assessment method for the first time. Qualitative data from surveys and focus groups on the students' examination experience were analysed, leading to the identification of engagement issues in the delivery of high-stakes computer-based assessments. The exam combined short answer open-response questions with multiple-choice-style items to assess knowledge and understanding of research methods. The findings suggest that engagement with computer-based testing depends, to a lesser extent, on students' general levels of digital literacy and, to a greater extent, on their information technology (IT) proficiency for assessment and their ability to adapt their test-taking strategies, including organisational and cognitive strategies, to the online assessment environment. The socialisation and preparation of students for computer-based testing therefore emerge as key responsibilities for instructors to address, with students requesting increased opportunities for practice and training to develop the IT skills and test-taking strategies necessary to succeed in computer-based examinations. These findings and their implications in terms of instructional responsibilities form the basis of a proposal for a framework for Learner Engagement with e-Assessment Practices.