Out-of-Distribution (OoD) segmentation is critical for safety-sensitive applications like autonomous driving. However, existing mask-based methods often suffer from boundary imprecision, inconsistent anomaly scores within objects, and false positives from background noise. We propose \textbf{\textit{Objectomaly}}, an objectness-aware refinement framework that incorporates object-level priors. Objectomaly consists of three stages: (1) Coarse Anomaly Scoring (CAS) using an existing OoD backbone, (2) Objectness-Aware Score Calibration (OASC) leveraging SAM-generated instance masks for object-level score normalization, and (3) Meticulous Boundary Precision (MBP) applying Laplacian filtering and Gaussian smoothing for contour refinement. Objectomaly achieves state-of-the-art performance on key OoD segmentation benchmarks, including SMIYC AnomalyTrack/ObstacleTrack and RoadAnomaly, improving both pixel-level (AuPRC up to 96.99, FPR$_{95}$ down to 0.07) and component-level (F1$-$score up to 83.44) metrics. Ablation studies and qualitative results on real-world driving videos further validate the robustness and generalizability of our method. Code will be released upon publication.