The only way to back up and restore is by uploading your data to Google's cloud servers, where your data is much more likely to be purloined than if you had just left your device unencrypted in the first place.
As an Android fan, let me just say that these problems do not just stop with encryption. Unless you root your phone, you can't back it up properly because Google doesn't let you have access to your own files on your own f'ing device. Apparently nobody sees a problem in the fact that users are forced to make the decisions to either run stock or be able to access all their files. I'm sure it's to reduce piracy or something, but it's a nightmare. Unless your apps keep their data in an accessible folder or you let them keep all your settings in the cloud (if they even support that), just upgrading your handset to this years Nexus is going to mean data loss.
I get that it makes the security stronger, but Android badly needs some kind of super-user mode that makes the entire filesystem accessible to selected apps.