Trustworthy language models should abstain from answering questions when they do not know the answer. However, the answer to a question can be unknown for a variety of reasons. Prior research has focused on the case in which the question is clear and the answer is unambiguous but possibly unknown. However, the answer to a question can also be unclear due to uncertainty of the questioner's intent or context. We investigate question answering from this perspective, focusing on answering a subset of questions with a high degree of accuracy, from a set of questions in which many are inherently ambiguous. In this setting, we find that the most reliable approach to calibration involves quantifying repetition within a set of sampled model outputs, rather than the model's likelihood or self-verification as used in prior work. % We find this to be the case across different types of uncertainty, varying model scales and both with or without instruction tuning. Our results suggest that sampling-based confidence scores help calibrate answers to relatively unambiguous questions, with more dramatic improvements on ambiguous questions.