How can we explain the uncertainty of clinical machine learning models to doctors? In this extended abstract, we propose uncertainty explanations for AI-enhanced clinical decision-making. In the last years, both explainability and uncertainty estimation have gained significant attention from the AI community. This has happened as a response to the black box criticism that AI faces because of its increasing application in high-stakes decision-making processes. We are particularly interested in the application of uncertainty explanations in healthcare settings, demonstrating it on the use case of automated sleep analysis. We show a proof-of-concept of the idea and identify the directions to further investigate in a follow-up study.