Hmmm.... invoke SendMessage, HWND_BROADCAST, WM_CLOSE, 0, 0 works just fine but IMHO it's not really "private" ;-)
Seriously: There are proper uses of HWND_BROADCAST, but an app that asks a server to send data should know the name and class of the server, and thus can restrict the request to what FindWindow returns; besides, if FindWindow returns 0, the app can tell the user with certainty that the server is not running, or even launch it automatically.