Insurance companies and Banks use models to assess the risk of their portfolios. No model, however, is perfect and model-based decisions might be highly sensitive to underlying model deviations. In our research, we develop a methodology that allows measuring the error one can make by using misspecified portfolio models. Our starting point is a given model of which we trust some characteristics such as the mean, the variance, the unimodality, the non-negativity, and the probabilities on certain (but not all) outcomes. We then provide the worst case, the best case, and the most plausible distribution for the portfolio loss such that it complies with the trusted characteristics. We provide analytical and numerical solutions and implement them in a software package that we will make publicly available.