Where are the calendar files stored on OS X (mountain lion) Server Calendar Service?
My users use the native Calendar service and I need to back this data up.
If you've enabled the Calendar service, by definition, collaborative user data are stored in the server PostGreSQL database.
You can access it by different way (network, socket), if you're looking to back this up, with Lion you could type in the Terminal :
With Mountain Lion, it seems PostGreSQL connection is slightly different, or the database table may have been renamed.
To have a basic understanding of how it works, you should explore pgsql database with a software like Navicat PostGreSQL or PgAdmin. Before editing pgsql, you should seriously consider to make a full backup of your server.