To backup your database, copy the .jdb files starting from the lowest numbered log file to the highest numbered log file to your backup media. Be sure to copy the bytes of the individual database files in order from the lowest to the highest. You do not have to close your database or otherwise cease database operations when you do this.
Restoring a JE database from a backup consists of closing your JE environment, copying archived log files back into your environment directory and then opening your JE environment again.
Note that whenever a JE environment is opened, JE runs normal recovery. This involves bringing your database into a consistent state given the changed data found in the database. If you are using transactions during normal operations, then JE automatically runs checkpoints for you so as to limit the time required to run this recovery. In any case, running normal recovery is a routine operation, while performing database restores is not.
For more information on JE backup and restores, and on checkpoints, see Backing up and Restoring Berkeley DB Java Edition Applications.