I wanted to switch my WSUS implementation over to https. Because I like https and there is rarely ever a reason not to use it. So, I set up my bindings in IIS and setup my group policy to point to the correct URL. After I got all of my clients updated with the new policy, they all started failing on checking for updates. They were getting a less than helpful "Not found error". The code is 0x80244019. While I was enabling the bindings for https, I was wondering what kind of services they were, because WCF requires special config for https. Otherwise it will spit out a 404. The fix turned out to be pretty easy. Reconfigure the WCF services for WSUS. In fact, in the web.config file, it tells you to do so.

To fix it, you'll need to edit the web.config file at C:\Program Files\Update Services\WebServices\ClientWebService\web.config. Search for bindingConfiguration="ClientWebServiceBinding". And now replace the ClientWebServiceBinding with SSL. There are 2 entries that will be replaced. In order to actually save the file, I had to take ownership of the file and modify the permissions. Once I changed the binding configuration, it all worked.
That was the only service that I saw that required any changing.