How Do I Post and then redirect to an external URL from ASP.Net?

ASP.NET server-side controls postback to their own page. This makes cases where you want to redirect a user to an external page, but need to post to that page for some reason (for authentication, for instance) a pain.

An HttpWebRequest works great if you don't want to redirect, and JavaScript is fine in some cases, but can get tricky if you really do need the server-side code to get the data together for the post.

So how do you both post to an external URL and redirect the user to the result from your ASP.NET codebehind code?