Unfortunately, there's no such thing as a simple "support CORS". The list of scenarios and options of what can be supported, for which methods, which headers etc. are very long. Alas, a whole bunch of APIs claiming to have CORS support also have a broken implementation, especially when it comes to proper support of pre-flighting (
https://developer.mozilla.org/en-US/docs/Web/HTTP/Access_control_CORS#Preflighted_requests). Which, IMHO, more of the fault of convoluted CORS spec than people trying to make sense of it, but anyway...
The CLI/curl-based solution Eric posted seems to be doing a proper job. There's also a web-based tool that doesn't seem to be too far off: