2 big options (besides hosting your own FMS of course):
- rent space to host your file or rent a dedicated FMS from one of the FM hosting providers
- use Microsoft Azure or Amazon's AWS to rent a server and install FMS on it yourself
We offer both shared and virtual dedicated server hosting accounts, specifically for FileMaker, and are in our 18th year of business. We offer a management package option with our virtual machines where we take care of setting up all the software as well as maintaining the server.
Please have a look at our services at http://www.pointinspace.com/ . Thanks!