Robotic manipulation requires accurate metric depth, yet commodity RGB-D cameras often fail on non-Lambertian objects such as transparent, reflective, and translucent materials, producing holes, structured noise, and biased depth. Most restoration methods produce only a single depth map, treating noisy and reliable regions uniformly for downstream tasks while ignoring regional uncertainty. We present UA-Depth, an uncertainty-aware depth restoration framework that iteratively co-refines depth and pixel-wise uncertainty, and uses uncertainty-gated features to suppress unreliable cues for stable updates. To strengthen zero-shot behavior, UA-Depth leverages a frozen depth foundation model as a prior to initialize missing or unreliable depth, and applies two-stage MAD-weighted log-depth scale normalization to reduce outlier bias in relative-to-metric alignment. We introduce an eight-dataset zero-shot benchmark across diverse scenes, materials, and sensors. Across these benchmarks, UA-Depth achieves the best mean rank among representative baselines, with particularly strong gains on datasets dominated by transparent and reflective objects. Beyond depth metrics, we demonstrate downstream improvements in category-level 6D pose estimation and 6D grasp synthesis by exploiting the predicted uncertainty. \emph{Code, models, and data for training and evaluation will be released upon publication.}

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