Artificial intelligence (AI) systems are poised to become deeply integrated into society. If developed responsibly, AI has potential to benefit humanity immensely. However, it also poses a range of risks, including risks of catastrophic accidents. It is crucial that we develop oversight mechanisms that prevent harm. This article outlines a framework for evaluating and auditing AI to provide assurance of responsible development and deployment, focusing on catastrophic risks. We argue that responsible AI development requires comprehensive auditing that is proportional to AI systems’ capabilities and available affordances. This framework offers recommendations toward that goal and may be useful in the design of AI auditing and governance regimes.