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 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 term of accuracy, a significant reliability gap persists. To addresses 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 enhance model reliability in offline mode. Extensive experiments under various settings demonstrate that ReliOcc significantly enhances model reliability while maintaining the accuracy of both geometric and semantic predictions. Importantly, our proposed approach exhibits robustness to sensor failures and out of domain noises during inference.