If you create an empty file with no file extension (on your desktop for example), then right click it, OSX/Finder offers various app choices to use to 'Open With..'

A lot of other text and code editors appear in this list (Atom, Visual Code, Sublime Text), but TextMate does not

It would be very useful if TM would register itself with OSX in the same way. 
I guess there's some way to do this manually, but if so, I haven't found it yet