Air traffic control uses Arrival Managers (AMANs) to schedule an inbound stream of aircraft. As these systems use predicted arrival times to optimize the planning for capacity and flight efficiency, the accuracy of these predictions is an important parameter in arrival planning. While prediction capabilities have improved, and are likely to improve more, it is unlikely that prediction error will disappear altogether. Especially in future scenarios with longer planning horizons, techniques will have to be found to support planning in the presence of prediction uncertainty. To enable working with uncertainty on a predicted arrival time, that uncertainty needs to be predicted itself. This paper proposes and tests a method to predict arrival time uncertainty based on historic prediction accuracy using currently available arrival time estimates.