Saving a file to another server

I've written a web application and it outputs a file to the server it did it like
string FName = Server.MapPath(@"~/MultiAccess/OutputFile/filename.txt");
This worked without any issues, now I've been told to save the file to another server on the same network, I wrote the following but it's not working
string FName = Server.MapPath(@"//ServerName//Output/filename.txt");
it's saying that c:/ServerName/Output/filename.txt does not exist
Any help appreciated