Post-deployment monitoring of artificial intelligence (AI) systems in health care is essential to ensure their safety, quality, and sustained benefit-and to support governance decisions about which systems to update, modify, or decommission. Motivated by these needs, we developed a framework for monitoring deployed AI systems grounded in the mandate to take specific actions when they fail to behave as intended. This framework, which is now actively used at Stanford Health Care, is organized around three complementary principles: system integrity, performance, and impact. System integrity monitoring focuses on maximizing system uptime, detecting runtime errors, and identifying when changes to the surrounding IT ecosystem have unintended effects. Performance monitoring focuses on maintaining accurate system behavior in the face of changing health care practices (and thus input data) over time. Impact monitoring assesses whether a deployed system continues to have value in the form of benefit to clinicians and patients. Drawing on examples of deployed AI systems at our academic medical center, we provide practical guidance for creating monitoring plans based on these principles that specify which metrics to measure, when those metrics should be reviewed, who is responsible for acting when metrics change, and what concrete follow-up actions should be taken-for both traditional and generative AI. We also discuss challenges to implementing this framework, including the effort and cost of monitoring for health systems with limited resources and the difficulty of incorporating data-driven monitoring practices into complex organizations where conflicting priorities and definitions of success often coexist. This framework offers a practical template and starting point for health systems seeking to ensure that AI deployments remain safe and effective over time.