SyncBackPro V9 (or later) supports file backup, sync and restore to/from a WebDav server.

SyncBack V8 (or earlier) does not include native support for WebDav. However using SyncBack with 3rd party products such as WebDrive (commercial) and NetDrive (freeware) it is possible. 

Note that if you are using SyncBackSE or SyncBackPro, then you may not be able to see the drive that is mapped to your WebDav storage. This is due to security changes in Windows. To use the WebDav drive you'll need to change SyncBackSE/Pro V8 (or earlier) so that it does not run elevated:

Note that running at the lowest security level means you cannot copy open/locked files, for example. It also means any profiles that are stored in the same folder as SyncBackSE/Pro cannot be used unless you have write permission to that folder (which is unlikely).