<p>I need to write robust code in .NET to enable a windows service (server 2003) to restart itself. What is the best way to so this? Is there some .NET API to do it?</p>

I don't think you can in a self-contained service (when you call Restart, it will stop the service, which will interrupt the Restart command, and it won't ever get started again). If you can add a second .exe (a Console app that uses the ServiceManager class), then you can kick off the standalone .exe and have it restart the service and then exit.
On second thought, you could probably have the service register a Scheduled Task (using the command-line 'at' command, for example) to start the service and then have it stop itself; that would probably work.