A key ethical challenge in Automated Essay Scoring (AES) is ensuring that scores are only released when they meet high reliability standards. Confidence modelling addresses this by assigning a reliability estimate measure, in the form of a confidence score, to each automated score. In this study, we frame confidence estimation as a classification task: predicting whether an AES-generated score correctly places a candidate in the appropriate CEFR level. While this is a binary decision, we leverage the inherent granularity of the scoring domain in two ways. First, we reformulate the task as an n-ary classification problem using score binning. Second, we introduce a set of novel Kernel Weighted Ordinal Categorical Cross Entropy (KWOCCE) loss functions that incorporate the ordinal structure of CEFR labels. Our best-performing model achieves an F1 score of 0.97, and enables the system to release 47% of scores with 100% CEFR agreement and 99% with at least 95% CEFR agreement — compared to ≈ 92 % CEFR agreement from the standalone AES model where we release all AM predicted scores.