I just found that my instance of Web Deploy agent stopped working and won't restart because of a missing SSL certificate.
When I try to start service IIS Manager (C:\Windows\system32\inetsrv\wmsvc.exe) it crashes and asks me to view Event Log.
Event log shows error IISWMSVC_STARTUP_UNABLE_TO_READ_CERTIFICATE related to certificate ID 608df89aa81d1ad2d87ee2dfcca76aa8abf92d11, which could be the self-signed certificate I might have deleted
We have an official *.example.com SSL certificate for our company that should be employed for Web Deploy too.
The question is: how do I tell Web Deploy to use a particular certificate?
Web Deploy utilizes the Web Management Service (WMSVC) and it sounds like something has happened with your WMSVC cert. If you go into IIS Manager and then go to "Management Service" from the server home pain.
From here you can select a new cert from the "SSL certificate" drop down list. You can also use this page to change what IP and port it is listening on if you wish.
After you update the SSL cert, then you should be able to restart the WMSVC service from this page.