Pressing Ctrl+Shift+Del
brings up the deletion dialog in almost all browsers (I\'ve tested IE, Firefox, and Chrome), where you can delete cookies,
There are two types of cookies: session and persistent. In your case, session cookies should be considered.
In IE 9 when you use Ctrl+Shift+Del option, you delete only persistent cookies.
If you want to delete session one, you must hit F12 to open the Developer Tools, click Cache and Delete session cookie
I had the same problem in IE9, where clearing browser cache and cookies would not actually delete the login cookie for my site. I finally resolved it by unchecking the first option in the dialog along with the cookies option (Preserve Favorites website data). (I'd include an image, but I'm new...)
First, close all IE windows and tabs, then open the "Internet Options" from the Control Panel, delete the cookies from there.
Also, as Chuck said, do not forget to uncheck the first option in the dialog along with the cookies option (Preserve Favorites website data).
You could also keep this window open to see the results of deleting procee : C:\Users\USERNAME\AppData\Roaming\Microsoft\Windows\Cookies (ie 11)
I assume your Authentication cookie is a session cookie. That will be deleted when the browser closes, and is typically stored in memory only. Since it's already that private, it makes little sense (from a privacy viewpoint) to delete it even quicker.
Now, some browsers may still delete it early. When they happen to have a unified cookie store, it's easier to just delete all cookies. But for browsers that handle session cookies separately, there's no good reason to duplicate the cookie deletion logic.