Overconfidence in deep learning models poses a significant risk in high-stakes medical imaging tasks, particularly in multi-label classification of chest X-rays, where multiple co-occurring pathologies must be detected simultaneously. This study introduces an uncertainty-aware framework for chest X-ray diagnosis based on a DenseNet-121 backbone, enhanced with two selective prediction mechanisms: entropy-based rejection and confidence interval-based rejection. Both methods enable the model to abstain from uncertain predictions, improving reliability by deferring ambiguous cases to clinical experts. A quantile-based calibration procedure is employed to tune rejection thresholds using either global or class-specific strategies. Experiments conducted on three large public datasets (PadChest, NIH ChestX-ray14, and MIMIC-CXR) demonstrate that selective rejection improves the trade-off between diagnostic accuracy and coverage, with entropy-based rejection yielding the highest average AUC across all pathologies. These results support the integration of selective prediction into AI-assisted diagnostic workflows, providing a practical step toward safer, uncertainty-aware deployment of deep learning in clinical settings.