Establishing reliable image correspondences is essential for many robotic vision problems. However, existing methods often struggle in challenging scenarios with large viewpoint changes or textureless regions, where incorrect cor- respondences may still receive high similarity scores. This is mainly because conventional models rely solely on fea- ture similarity, lacking an explicit mechanism to estimate the reliability of predicted matches, leading to overconfident errors. To address this issue, we propose SURE, a Semi- dense Uncertainty-REfined matching framework that jointly predicts correspondences and their confidence by modeling both aleatoric and epistemic uncertainties. Our approach in- troduces a novel evidential head for trustworthy coordinate regression, along with a lightweight spatial fusion module that enhances local feature precision with minimal overhead. We evaluated our method on multiple standard benchmarks, where it consistently outperforms existing state-of-the-art semi-dense matching models in both accuracy and efficiency. our code will be available on https://github.com/LSC-ALAN/SURE.