The ability to classify images accurately and efficiently is dependent on having access to large labeled datasets and testing on data from the same domain that the model is trained on. Classification becomes more challenging when dealing with new data from a different domain, where collecting a large labeled dataset and training a new classifier from scratch is time-consuming, expensive, and sometimes infeasible or impossible. Cross-domain classification frameworks were developed to handle this data domain shift problem by utilizing unsupervised image-to-image (UI2I) translation models to translate an input image from the unlabeled domain to the labeled domain. The problem with these unsupervised models lies in their unsupervised nature. For lack of annotations, it is not possible to use the traditional supervised metrics to evaluate these translation models to pick the best-saved checkpoint model. In this paper, we introduce a new method called Pseudo Supervised Metrics that was designed specifically to support cross-domain classification applications contrary to other typically used metrics such as the FID which was designed to evaluate the model in terms of the quality of the generated image from a human-eye perspective. We show that our metric not only outperforms unsupervised metrics such as the FID, but is also highly correlated with the true supervised metrics, robust, and explainable. Furthermore, we demonstrate that it can be used as a standard metric for future research in this field by applying it to a critical real-world problem (the boiling crisis problem).