Deep learning models in robotics often output point estimates with poorly calibrated confidences, offering no native mechanism to quantify predictive reliability under novel, noisy, or out-of-distribution inputs. Conformal prediction (CP) addresses this gap by providing distribution-free coverage guarantees, yet its reliance on fixed nonconformity scores ignores context and can yield intervals that are overly conservative or unsafe. We address this with Learnable Conformal Prediction (LCP), which replaces fixed scores with a lightweight neural function that leverages geometric, semantic, and task-specific features to produce context-aware uncertainty sets. LCP maintains CP's theoretical guarantees while reducing prediction set sizes by 18% in classification, tightening detection intervals by 52%, and improving path planning safety from 72% to 91% success with minimal overhead. Across three robotic tasks on seven benchmarks, LCP consistently outperforms Standard CP and ensemble baselines. In classification on CIFAR-100 and ImageNet, it achieves smaller set sizes (4.7-9.9% reduction) at target coverage. For object detection on COCO, BDD100K, and Cityscapes, it produces 46-54% tighter bounding boxes. In path planning through cluttered environments, it improves success to 91.5% with only 4.5% path inflation, compared to 12.2% for Standard CP. The method is lightweight (approximately 4.8% runtime overhead, 42 KB memory) and supports online adaptation, making it well suited to resource-constrained autonomous systems. Hardware evaluation shows LCP adds less than 1% memory and 15.9% inference overhead, yet sustains 39 FPS on detection tasks while being 7.4 times more energy-efficient than ensembles.