Check for a Save-Singleplayer or Save-Multiplayer folder (as approrpiate) in the location below, and just copy the files to the same place on the other machine. Make sure you have the same game version on both.
Vista:
C:\Users\your username\AppData\Local\Ironclad Games\Sins of a Solar Empire\
XP:
C:\Documents and Settings\your username\Local Settings\Application Data\Ironclad Games\Sins of a Solar Empire\
Please note that some of these directories are hidden by default. To unhide them, go to Control Panel -> Folder Options -> View and set yourself to view hidden files and folders.
