  Since neural classifiers are known to be sensitive to adversarial
perturbations that alter their accuracy, \textit{certification methods} have
been developed to provide provable guarantees on the insensitivity of their
predictions to such perturbations. Furthermore, in safety-critical
applications, the frequentist interpretation of the confidence of a classifier
(also known as model calibration) can be of utmost importance. This property
can be measured via the Brier score or the expected calibration error. We show
that attacks can significantly harm calibration, and thus propose certified
calibration as worst-case bounds on calibration under adversarial
perturbations. Specifically, we produce analytic bounds for the Brier score and
approximate bounds via the solution of a mixed-integer program on the expected
calibration error. Finally, we propose novel calibration attacks and
demonstrate how they can improve model calibration through \textit{adversarial
calibration training}.
