We present a framework for migrating production Large Language Model (LLM) based systems when the underlying model reaches end-of-life or requires replacement. The key contribution is a Bayesian statistical approach that calibrates automated evaluation metrics against human judgments, enabling confident model comparison even with limited manual evaluation data. We demonstrate this framework on a commercial question-answering system serving 5.3M monthly interactions across six global regions; evaluating correctness, refusal behavior, and stylistic adherence to successfully identify suitable replacement models. The framework is broadly applicable to any enterprise deploying LLM-based products, providing a principled, reproducible methodology for model migration that balances quality assurance with evaluation efficiency. This is a capability increasingly essential as the LLM ecosystem continues to evolve rapidly and organizations manage portfolios of AI-powered services across multiple models, regions, and use cases.