Multi-Agent Systems (MAS) are a promising paradigm for improving the reasoning capabilities of large language models, yet they remain prone to hallucinations and erroneous outputs. Uncertainty Quantification (UQ) is crucial for assessing system reliability, but existing methods are largely designed for single-agent settings; how to exploit MAS structure for UQ while keeping inference cost-neutral remains underexplored. We propose UMAS, a parameter-free, cost-neutral, system-level UQ framework that estimates the credibility of inter-agent influence from each generation's intrinsic confidence. UMAS uses these credibility signals to modulate how uncertainty is updated at each node, and then aggregates node-level uncertainty into a system-level estimate. Extensive evaluations on Debate and DyLAN across diverse benchmarks show that UMAS consistently outperforms state-of-the-art baselines by an average of 10.54 AUROC points. Beyond uncertainty estimation, UMAS enables hallucination detection and uncertainty-aware answer selection, improving MAS accuracy by up to 12.6 points on specific tasks while enhancing reliability. Code is available at https://github.com/Dby52-04/UMAS.

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