Reinforcement learning with verifiable rewards (RLVR) has recently demonstrated substantial gains in reasoning capabilities of vision–language models (VLMs). However, existing RLVR paradigms rely on deterministic rewards that implicitly penalize uncertainty expression and abstention, causing VLMs to overproduce speculative answers and degrading reliability. Through quantitative analysis, we find that vanilla RLVR, while effective in improving reasoning accuracy, significantly impairs VLMs’ ability to appropriately abstain from unanswerable queries. To systematically address this, we introduce Reliable-V-Bench, a new benchmark designed to evaluate VLMs’ abstaining capacity on challenging and realistic unanswerable visual questions. We further propose Reliable-V-RL, a reliability-aware RL framework that incorporates unanswerable and ambiguous visual questions into training, guided by a fine-grained, rubric-based reward mechanism that encourages VLMs to jointly optimize reasoning accuracy and reliable judgment. Experimental results demonstrate that Reliable-V-RL substantially improves the reliability and abstention capability of VLMs without sacrificing performance on standard multimodal benchmarks.