Modern neural networks have found to be miscalibrated in terms of confidence calibration, i.e., their predicted confidence scores do not reflect the observed accuracy or precision. Recent work has introduced methods for post-hoc confidence calibration for classification as well as for object detection to address this issue. Especially in safety critical applications, it is crucial to obtain a reliable self-assessment of a model. But what if the calibration method itself is uncertain, e.g., due to an insufficient knowledge base? We introduce Bayesian confidence calibration - a framework to obtain calibrated confidence estimates in conjunction with an uncertainty of the calibration method. Commonly, Bayesian neural networks (BNN) are used to indicate a network's uncertainty about a certain prediction. BNNs are interpreted as neural networks that use distributions instead of weights for inference. We transfer this idea of using distributions to confidence calibration. For this purpose, we use stochastic variational inference to build a calibration mapping that outputs a probability distribution rather than a single calibrated estimate. Using this approach, we achieve state-of-the-art calibration performance for object detection calibration. Finally, we show that this additional type of uncertainty can be used as a sufficient criterion for covariate shift detection. All code is open source and available at https://github.com/EFS-OpenSource/calibration-framework.