A machine learning model is traditionally considered robust if its prediction remains (almost) constant under input perturbations with small norm. However, real-world tasks like molecular property prediction or point cloud segmentation have inherent equivariances,such as equivariance to rotation or permutation. In such tasks, even perturbations with large norm do not necessarily change an input's semantic content. Furthermore, there are perturbations for which a model's prediction explicitly needs to change. For the first time, we propose a sound notion of adversarial robustness that accounts for task equivariance. We then demonstrate that model equivariance improves robustness and that randomized smoothing can be used to even make models provably robust while preserving their equivariances. We additionally derive the first graph edit distance certificates, i.e. sound robustness guarantees for isomorphism equivariant tasks like node classification. Overall, developing a sound notion of robustness for equivariant tasks is an important prerequisite for future work at the intersection of robust and geometric machine learning.