Depending on the configuration the UPS can initiate the shutdown command OR the Windows server can initiate the shut down command. If the UPS is managed check its configuration to issue the shut down command.
ON the Server:
Once connected in the control panel on the 2003 server go to power options. Then click on the UPS tab...check enable all notifications (select the seconds between power failure and first notification...5 is default).
The key is the Critical Alarm section...minutes on battery before critical alarm. You have to estimate the minutes the UPS can carry the load and subtract a few minutes. At that point the Next instruct the computer to "Shut down"