Being cautious is crucial for enhancing the trustworthiness of machine learning systems integrated into decision-making pipelines. Although calibrated probabilities help in optimal decision-making, perfect calibration remains unattainable, leading to estimates that fluctuate between under- and overconfidence. This becomes a critical issue in high-risk scenarios, where even occasional overestimation can lead to extreme expected costs. In these scenarios, it is important for each predicted probability to lean towards underconfidence, rather than just achieving an average balance. In this study, we introduce the novel concept of cautious calibration in binary classification. This approach aims to produce probability estimates that are intentionally underconfident for each predicted probability. We highlight the importance of this approach in a high-risk scenario and propose a theoretically grounded method for learning cautious calibration maps. Through experiments, we explore and compare our method to various approaches, including methods originally not devised for cautious calibration but applicable in this context. We show that our approach is the most consistent in providing cautious estimates. Our work establishes a strong baseline for further developments in this novel framework.