Estimating test performance of software AI-based medical devices under distribution shifts is crucial for evaluating safety, efficiency, and usability prior to clinical deployment~\cite{fda}.Due to the nature of regulated medical device software and the difficulty in acquiring large amounts of labeled medical datasets, we consider the task of predicting test accuracy of an arbitrary black-box model on an unlabeled target domain \textit{without} modification to the original training process or any distributional assumptions of the original source data (i.e. we treat the model as a black-box'' and only use the predicted output responses).We propose ablack-box'' test estimation technique based on conformal prediction and evaluate against other methods on three medical imaging datasets (mammography, dermatology, and histopathology) under several clinically relevant types of distribution shift (institution, hardware scanner, atlas, hospital).We hope that by promoting practical and effective estimation techniques for black-box models, manufacturers of medical devices will develop more standardized and realistic evaluation procedures to improve robustness and trustworthiness of clinical AI tools.