Predicting human trajectories is essential for the safe operation of autonomous vehicles, yet current data-driven models often lack robustness in case of noisy inputs such as adversarial examples or imperfect observations. Although some trajectory prediction methods have been developed to provide empirical robustness, these methods are heuristic and do not offer guaranteed robustness. In this work, we propose a certification approach tailored for trajectory prediction that provides guaranteed robustness. To this end, we address the unique challenges associated with trajectory prediction, such as unbounded outputs and multi-modality. To mitigate the inherent performance drop through certification, we propose a diffusion-based trajectory denoiser and integrate it into our method. Moreover, we introduce new certified performance metrics to reliably measure the trajectory prediction performance. Through comprehensive experiments, we demonstrate the accuracy and robustness of the certified predictors and highlight their advantages over the non-certified ones. The code is available online: https://s-attack.github.io/