A drawback of the projection approach is that both coverage and robust credibility may be strictly above their nominal level. Following the work of Kaido, Molinari, and Stoye (2016), we ‘calibrate’the radius of the Wald ellipsoid to guarantee that—for a given posterior on the reduced-form parameters—the robust Bayesian credibility of the projection method is exactly 1− α. If the bounds of the identified set are differentiable, our calibrated projection also covers the identified set with probability 1− α. We illustrate the main results of the paper using the demand/supply-model for the US labor market in Baumeister and Hamilton (2015).