Many defenses against adversarial attacks (e.g. robust classifiers, randomization, or image purification) use countermeasures put to work only after the attack has been crafted. We adopt a different perspective to introduce A^5 (Adversarial Augmentation Against Adversarial Attacks), a novel framework including the first certified preemptive defense against adversarial attacks. The main idea is to craft a defensive perturbation to guarantee that any attack (up to a given magnitude) towards the input in hand will fail. To this aim, we leverage existing automatic perturbation analysis tools for neural networks. We study the conditions to apply A^5 effectively, analyze the importance of the robustness of the to-be-defended classifier, and inspect the appearance of the robustified images. We show effective on-the-fly defensive augmentation with a robustifier network that ignores the ground truth label, and demonstrate the benefits of robustifier and classifier co-training. In our tests, A^5 consistently beats state of the art certified defenses on MNIST, CIFAR10, FashionMNIST and Tinyimagenet. We also show how to apply A^5 to create certifiably robust physical objects. The released code at https://github.com/NVlabs/A5 allows experimenting on a wide range of scenarios beyond the man-in-the-middle attack tested here, including the case of physical attacks.