Title: Improved Uncertainty Post-Calibration via Rank Preserving Transforms. Abstract: Modern machine learning models with high accuracy often exhibit poor uncertainty calibration: the output probabilities of the model do not reflect its accuracy, and tend to be over-confident. Existing post-calibration methods such as temperature scaling recalibrate a trained model using rather simple calibrators with one or few parameters, which can have a rather limited capacity. In this paper, we propose Neural Rank Preserving Transforms (NRPT), a new post-calibration method that adjusts the output probabilities of a trained classifier using a calibrator of higher capacity, while maintaining its prediction accuracy. NRPT learns a calibrator that preserves the rank of the probabilities through general monotonic transforms, individualizes to the original input, and allows learning with any loss function that encourages calibration. We show experimentally that NRPT improves the expected calibration error (ECE) significantly over existing post-calibration methods such as (local) temperature scaling on large-scale image and text classification tasks. The performance of NRPT can further match ensemble methods such as deep ensembles, while being much more parameter-efficient. We further demonstrate the improved calibration ability of NRPT beyond the ECE metric, such as accuracy among top-confidence predictions, as well as optimizing the tradeoff between calibration and sharpness.