Response caching is an effective way to reduce request latency and back end load. Microsoft is working on enabling you to use an external Redis-compatible cache, for example, Azure Redis Cache. You'll get full control over the size and content of the cache, be able to scale independently from their Azure API Management instances, and share it across multiple API Management instances, as well as preload and evict cached data as needed.
To vote on this development and share your thoughts, please see Use external cache with Azure API Management.