Many embedded systems are subject to temporal constraints that require advance guarantees on meeting deadlines. Such systems rely on static analysis to safely bound worst-case execution (WCET) bounds of tasks. Designers of these systems are forced to avoid state-of-the-art processors due to their inherent architectural complexity (such as out-oforder instruction scheduling) that results in non-determinism. This work addresses this problem by providing novel pipeline analysis techniques for characterizing the worst-case behavior of real-time systems on modern processor architectures. We introduce methods to capture ("snapshot") pipeline state and to subsequently perform a "merge" of previously captured snapshots. We prove that our pipeline analysis correctly preserves worst-case timing behavior on out-of-order (OOO) processor pipelines. We further specifically show that anomalous pipeline effects, effectively dilating timing, are preserved by our method. To the best of our knowledge, this method of pipeline analysis and interactions between hardware/ software for obtaining WCET bounds on OOO processors is the first of its kind.