We show that differentially private stochastic gradient descent (DP-SGD) can yield poorly calibrated, overconfident deep learning models. This represents a serious issue for safety-critical applications, e.g. in medical diagnosis. We highlight and exploit parallels between stochastic gradient Langevin dynamics, a scalable Bayesian inference technique for training deep neural networks,and DP-SGD, in order to train differentially private, Bayesian neural networks with minor adjustments to the original (DP-SGD) algorithm.Our approach provides considerably more reliable uncertainty estimates than DP-SGD, as demonstrated empirically by a reduction in expected calibration error (MNIST∼5-fold, Pediatric Pneumonia Dataset∼2-fold).