I notice this is a very old question, but the given answers are not ideal and it's already been necroed. All the existing answers require typing archaic commands and knowing the exact path to your executable. An ideal option would make this possible using the same process you already use for privilege escalation.
If you have a non-Home edition of Windows (Vista thru 10) you can use the Security Policy Manager to make it prompt you to give your password whenever elevation occurs. It also gives you the option to select a completely different user and enter their password... which will cause the elevated process to run as them.
Simply open the start menu and type secpol.msc
and hit enter to launch it (if it's available). You're looking for Local Policies
> Security Options
> User Account Control: Behavior of the elevation prompt for administrators in Admin Approval Mode
> Prompt for credentials
. Vista has a similar option that doesn't mention "Admin Approval Mode" but it does the same thing.
I think this is a much more natural option than the other's offered here and is rather reminiscent of gksudo on *nix. But if your edition of Windows doesn't include secpol.msc you will have to do some registry hackery to enable it.
start-process
command might be able to do this.