In high-stakes decision-making tasks within legal NLP, such as Case Outcome Classification (COC), quantifying a model’s predictive confidence is crucial. Confidence estimation enables humans to make more informed decisions, particularly when the model’s certainty is low, or where the consequences of a mistake are significant. However, most existing COC works prioritize high task performance over model reliability. This paper conducts an empirical investigation into how various design choices—including pre-training corpus, confidence estimator and fine-tuning loss—affect the reliability of COC models within the framework of selective prediction. Our experiments on the multi-label COC task, focusing on European Court of Human Rights (ECtHR) cases, highlight the importance of a diverse yet domain-specific pre-training corpus for better calibration. Additionally, we demonstrate that larger models tend to exhibit overconfidence, Monte Carlo dropout methods produce reliable confidence estimates, and confident error regularization effectively mitigates overconfidence. To our knowledge, this is the first systematic exploration of selective prediction in legal NLP. Our findings underscore the need for further research on enhancing confidence measurement and improving the trustworthiness of models in the legal domain.