The proxy server could not handle the request: Error during SSL Handshake with remote server

Symptoms

You may see an error like the following on sites that have been recently transferred to a new server.

Proxy Error
The proxy server could not handle the request
Reason: Error during SSL Handshake with remote server

Description 

This will happen if the site still resolves to the old server, and the SSL installed for the site on the new server is invalid for some reason or there is no SSL installed for it.

Workaround

The SSL issue will need to be resolved on the new server. If the site is intended to use AutoSSL on the new server, the site's DNS will need to be updated to point to the new server.

Related

How to find out where a domain's DNS is hosted