CloudBerry Backup now warns about EFS encrypted files instead of backing them up I'm not expecting some magic solution. Of course the EFS certificates would need to be backed up. In a Windows domain scenario, the best solution would likely be backing up the recovery agent's private key (since the default recovery agent is the admin account on the first domain controller).
While it might be possible for backup software with sufficient privileges to handle this key backup automatically, I'm certainly OK with having to do a one-time manual export of a recovery agent key to a file that could then be backed up along with all the other files.
But all of that is moot if the software refuses to backup EFS encrypted files at all. There are certainly other apps that have successfully backed up EFS files without decrypting them. The trick is using an EFS specific API from Microsoft. Bvckup2 is one such software (great software, but only supports local network source/destinations). You can google "bvckup2 efs" and the top result should be a forum where there are details and a link to Microsoft's EFS API.
You ask why I am using EFS. I'm not, nor do I like it. I'm actually about to disable support for it domain-wide with GPOs for most of my clients. The problem is that, unless it is disabled in the domain, any domain user can choose to use it. So any clients with users that already have EFS-encrypted files will still have those files. It is what it is.
In regards to the image backup, there is a lot more flexibility for a variety of things (like retention) that you can do with file-level backups, so I don't see an image backup as being a viable workaround at this point. Bottom line, it doesn't seem like it would be that hard to just back up the files as-is using Microsoft's EFS API in a file-level backup (along with warnings for any EFS files in regards to the need for a recovery key).