Reinforcement learning (RL) finetuning is crucial to aligning large language models (LLMs), but the process is notoriously unstable and exhibits high variance across model checkpoints. In practice, selecting the best checkpoint is challenging: evaluating checkpoints on the validation set during training is computationally expensive and requires a good validation set, while relying on the final checkpoint provides no guarantee of good performance. We introduce an uncertainty-guided approach for checkpoint selection (UGCS) that avoids these pitfalls. Our method identifies hard question-answer pairs using per-sample uncertainty and ranks checkpoints by how well they handle these challenging cases. By averaging the rewards of the top-uncertain samples over a short training window, our method produces a stable and discriminative signal without additional forward passes or significant computation overhead. Experiments across three datasets and three LLMs demonstrate that it consistently identifies checkpoints with stronger generalization, outperforming traditional strategies such as relying on training or validation performance. These results highlight that models solving their hardest tasks with low uncertainty are the most reliable overall.