The host does not need to "save" at all.
When the host loads the game, the only option will be end turn, and SE4 will automatically process, save and then exit when end turn is pressed.
Error Messages about incorrect turn files, etc will pop up as soon as you press end turn, and you will have the option to abort processing at that time.
The savegame will be updated, and can be emailed to all of the players again for the next turn.
All of that hosting can be done automatically by the PBW server. See
www.pbw.cc