Container terminals across the world sort the containers in the stacks in their yard in a process called pre-marshalling to ensure their efficient retrieval for onward transport. The container pre-marshalling problem (CPMP) has mainly been considered from a deterministic perspective, with containers being assigned an exact exit time from the yard. However, exact exit times are rarely known, and most containers can at best be assigned a time interval in which they are expected to leave. We propose a method for solving the robust CPMP (RCPMP) to optimality that computes a relaxation of the robust problem and leverages this within a solution procedure for the deterministic CPMP. Our method outperforms the state-of-the-art approach on a dataset of 900 RCPMP instances, finding solutions in many cases in under a second.