Ensuring safety in deep reinforcement learning is challenging, as formal methods that provide strong guarantees often fail to scale to complex, high-dimensional systems. We introduce RAMPS, a scalable shielding framework that pairs a general-purpose, learned linear dynamics model with a robust, multi-step Control Barrier Function (CBF) for real-time safety interventions. Experiments show RAMPS significantly reduces safety violations in high-dimensional environments compared to state-of-the-art methods, without sacrificing task performance.