Vision-centric semantic occupancy prediction plays a crucial role in autonomous driving, which requires accurate and reliable predictions from low-cost sensors. Although having notably narrowed the accuracy gap with LiDAR, there is still few research effort to explore the reliability and calibration in predicting semantic occupancy from camera. In this paper, we conduct a comprehensive evaluation of existing semantic occupancy prediction models from a reliability perspective for the first time. Despite the gradual alignment of camera-based models with LiDAR in terms of accuracy, a significant reliability gap still persists. To address this concern, we propose ReliOcc, a method designed to enhance the reliability of camera-based occupancy networks. ReliOcc provides a plug-and-play scheme for existing models, which integrates hybrid uncertainty from individual voxels with sampling-based noise and relative voxels through mix-up learning. Besides, an uncertainty-aware calibration strategy is devised to further improve model reliability in offline mode. Extensive experiments under various settings demonstrate that ReliOcc significantly enhances the reliability of learned model while maintaining the accuracy for both geometric and semantic predictions. Notably, our proposed approach exhibits robustness to sensor failures and out of domain noises during inference.