If you have the database (,rmdb) file backed up (and backups are always a good idea), then you should be OK.
Ideally you would backup the whole project directory, as background and waypoint image files are also stored in there.
To use your backup, simply copy the file (or directory) somewhere and browse to it in RM to open it. The big issue might be paths of the original sonar log files. RM expects these to be in the same location from which they were imported, and they are needed for sonar viewer and sidescan operations. If they are not in their original locations, then RM will prompt you to browse for them and the location is updated in the DB. This can get very tedious for a lot of files, so it is much better to make sure they are available in the same location.