Semantic segmentation networks (SSNs) are central to safety-critical applications such as medical imaging and autonomous driving, where robustness under uncertainty is essential. However, existing probabilistic verification methods often fail to scale with the complexity and dimensionality of modern segmentation tasks, producing guarantees that are overly conservative and of limited practical value. We propose a probabilistic verification framework that is architecture-agnostic and scalable to high-dimensional input-output spaces. Our approach employs conformal inference (CI), enhanced by a novel technique that we call the \textbf{clipping block}, to provide provable guarantees while mitigating the excessive conservatism of prior methods. Experiments on large-scale segmentation models across CamVid, OCTA-500, Lung Segmentation, and Cityscapes demonstrate that our framework delivers reliable safety guarantees while substantially reducing conservatism compared to state-of-the-art approaches on segmentation tasks. We also provide a public GitHub repository (https://github.com/Navidhashemicodes/SSN_Reach_CLP_Surrogate) for this approach, to support reproducibility.