Recent advancements in large language models (LLMs) have shifted the post-training paradigm from traditional instruction tuning and human preference alignment toward reinforcement learning (RL) focused on reasoning capabilities. However, most current methods rely on rule-based evaluations of answer correctness, overlooking the importance of confidence-aware reasoning, especially for small to medium-sized models. These models often receive rewards for speculative answers without generating coherent reasoning chains. To address this limitation, we propose a novel confidence-based reward model tailored for enhancing STEM reasoning capabilities. Unlike conventional approaches, our model penalizes not only incorrect answers but also low-confidence correct responses, thereby promoting more robust and logically consistent reasoning. We validate the effectiveness of our approach through static evaluations, Best-of-N inference tests, and PPO-based RL training. Our method outperforms several state-of-the-art open-source reward models across diverse STEM benchmarks. We release our codes and model in https://github.com/qianxiHe147/C2RM.