There's live migration of Solaris 11 Kernel Zones, but that's something different entirely.
Migration of traditional zones wasn't live - either put it on shared storage or bundle it up and copy to a new host, then remove from source and import at the destination. We never migrated zones - rather migrate just the app, which means you don't need to sync the OS. If you use zfs to sync the data+app, you can get migration time down to a few seconds.