In this paper, we investigate the problem of predictive confidence in face and kinship verification. Most existing face and kinship verification methods focus on accuracy performance while ignoring confidence estimation for their prediction results. However, confidence estimation is essential for modeling reliability in such high-risk tasks. To address this issue, we first introduce a novel yet simple confidence measure for face and kinship verification, which allows the verification models to transform the similarity score into a confidence score for a given face pair. We further propose a confidence-calibrated approach called angular scaling calibration (ASC). ASC is easy to implement and can be directly applied to existing face and kinship verification models without model modifications, yielding accuracy-preserving and confidence-calibrated probabilistic verification models. To the best of our knowledge, our approach is the first general confidence-calibrated solution to face and kinship verification in a modern context. We conduct extensive experiments on four widely used face and kinship verification datasets, and the results demonstrate the effectiveness of our approach.