Successful deployment in uncertain, real-world environments requires that deep learning models can be efficiently and reliably modified in order to adapt to unexpected issues. However, the current trend toward ever-larger models makes standard retraining procedures an ever-more expensive burden. For this reason, there is growing interest in model editing, which enables computationally inexpensive, interpretable, post-hoc model modifications. While many model editing techniques are promising, research on the properties of edited models is largely limited to evaluation of validation accuracy. The robustness of edited models is an important and yet mostly unexplored topic. In this paper, we employ recently developed techniques from the field of deep learning robustness to investigate both how model editing affects the general robustness of a model, as well as the robustness of the specific behavior targeted by the edit. We find that edits tend to reduce general robustness, but that the degree of degradation depends on the editing algorithm chosen. In particular, robustness is best preserved by more constrained techniques that modify less of the model. Motivated by these observations, we introduce two new model editing algorithms, direct low-rank model editing and 1-layer interpolation (1-LI), which each exhibit strong generalization performance.