As noted in the Fiddler book,

Sessions rerouted from one hostname to another using the Host Remapping tool are rendered with a light blue background in the Web Sessions list. HTTPS Sessions that have been rerouted have the X-IgnoreCertCNMismatch and X-OverrideCertCN Session Flags set to avoid raising “Certificate Name Mismatch” errors.

However, there's a bug. In the HostsFile.cs code, there's are several places that look like:

            if (oS.isTunnel) {

                oS["x-overrideCertCN"] = oS.hostname;
                oS["X-IgnoreCertCNMismatch"] = "HOSTS-Ext";
            }

This usually works for browser traffic going through Fiddler (because the HTTPS handshake is typically conducted on the CONNECT tunnel). However, it doesn't work (and the user is spammed with cert error warnings) if the traffic is sent from Fiddler itself (e.g. via Composer or using the "Reissue requests" context menu item). 

The code should look like this:

            if (oS.isHTTPS || oS.isTunnel) {

                oS["x-overrideCertCN"] = oS.hostname;
                oS["X-IgnoreCertCNMismatch"] = "HOSTS-Ext";

           }