In the periodic event scheduling problem, periodically reoccurring events need to be scheduled, subject to constraints on the resulting time differences. A typical application for this type of problem relates to train schedules, which have to repeat every hour for passenger convenience. As external disruptions may occur, robustness considerations need to be included in the scheduling process. In this work, we present a recovery approach for instances where integer programming methods can be applied, and a bi-criteria local search algorithm for large-scale instances. In computational experiments, we compare solutions calculated using the recovery approach to risk-averse and to risk-oblivious solutions. Our results suggest that the solutions generated by our approach have a favorable trade-off between cost and robustness. Furthermore, we compare the local search algorithm to a simplified approach that includes the desired robustness level as a hard constraint. The experiments show that our algorithm finds an improved set of non-dominated solutions within equal computation times.