As neural network classifiers are deployed in real-world applications, it is crucial that their failures can be detected reliably. One practical solution is to assign confidence scores to each prediction, then use these scores to filter out possible misclassifications. However, existing confidence metrics are not yet sufficiently reliable for this role. This paper presents a new framework that produces a quantitative metric for detecting misclassification errors. This framework, RED, builds an error detector on top of the base classifier and estimates uncertainty of the detection scores using Gaussian Processes. Experimental comparisons with other error detection methods on 125 UCI datasets demonstrate that this approach is effective. Further implementations on two probabilistic base classifiers and two large deep learning architecture in vision tasks further confirm that the method is robust and scalable. Third, an empirical analysis of RED with out-of-distribution and adversarial samples shows that the method can be used not only to detect errors but also to understand where they come from. RED can thereby be used to improve trustworthiness of neural network classifiers more broadly in the future.