Modern software programs are built on stacks that are often undergoing changes that introduce updates and improvements, but may also break any project that depends upon them. In this paper we explore the use of Large Language Models (LLMs) for code migration, specifically the problem of maintaining compatibility with a dependency as it undergoes major and minor semantic version changes. We demonstrate, using metrics such as test coverage and change comparisons, that contexts containing diffs can significantly improve performance against out of the box LLMs and, in some cases, perform better than using code. We provide a dataset to assist in further development of this problem area, as well as an open-source Python package, AIMigrate, that can be used to assist with migrating code bases. In a real-world migration of TYPHOIDSIM between STARSIM versions, AIMigrate correctly identified 65% of required changes in a single run, increasing to 80% with multiple runs, with 47% of changes generated perfectly.