Clone a system to an encrypted drive

[Chris Adams]

I have a running Fedora 21 system.  I would like to make a backup of it
to a USB drive, a clone that can be booted.  I know how to do all the
"normal" stuff (partition, LVM, mkfs, rsync, and GRUB), but I'd like the
USB drive to be encrypted, and I don't know how to set that up manually
(I haven't messed with encrypted filesystems under Linux before).

The system I'm backing is also headless, so no GUI tools.

Pointers, tips, suggestions?  Thanks.
-- 
Chris Adams <linux at cmadams.net>