Dense feature matching methods aim to estimate a dense correspondence field between images. Inaccurate correspondence can occur due to the presence of unmatchable region, necessitating the need for certainty measurement. This is typically addressed by training a binary classifier to decide whether each predicted correspondence is reliable. However, deep neural network-based classifiers can be vulnerable to image corruptions or perturbations, making it difficult to obtain reliable matching pairs in corrupted scenario. In this work, we propose an evidential deep learning framework to enhance the robustness of dense matching against corruptions. We modify the certainty prediction branch in dense matching models to generate appropriate belief masses and compute the certainty score by taking expectation over the resulting Dirichlet distribution. We evaluate our method on a wide range of benchmarks and show that our method leads to improved robustness against common corruptions and adversarial attacks, achieving up to 10.1\% improvement under severe corruptions.