Personalized federated learning allows for clients in a distributed system to train a neural network tailored to their unique local data while leveraging information at other clients. However, clients' models are vulnerable to attacks during both the training and testing phases. In this paper we address the issue of adversarial clients crafting evasion attacks at test time to deceive other clients. For example, adversaries may aim to deceive spam filters and recommendation systems trained with personalized federated learning for monetary gain. The adversarial clients have varying degrees of personalization based on the method of distributed learning, leading to a "grey-box" situation. We are the first to characterize the transferability of such internal evasion attacks for different learning methods and analyze the trade-off between model accuracy and robustness depending on the degree of personalization and similarities in client data. We introduce a defense mechanism, pFedDef, that performs personalized federated adversarial training while respecting resource limitations at clients that inhibit adversarial training. Overall, pFedDef increases relative grey-box adversarial robustness by 62% compared to federated adversarial training and performs well even under limited system resources.