There's a number of different Linuxes, installed on each of my computers.  Each Linux lives in its own partition and is totaly independent from any other one.  A huge data partition with user data files in it is the only thing shared between them, used by all installed Linuxes.

FSArchiver is added to each installed Linux.

The simple thing is - never backup/restore a mounted partition.  Nothing else.

For example, there are A, B, C, D Linuxes installed in their own partitions.  I want to backup A and B ones.  I simply boot into C or D, and run FSArchiver from them, backing up A and B either separately, in two separated archives, or put them both in a single archive.

To restore A or B, I boot again into C or D, and restore either A or B, or both.

The important thing to note here is that while C or D are running, A and B remain unmounted.  So I can backup, restore, do whatever I want with partitions, corresponding to A and B.

FSArchiver archives are kept on an external USB disk.

Finally, I have a bootable USB flash stick with SystemRescueCD on it.  FSArchiver is included in each and every SystemRescueCD release.  In the worst case, when internal disk is totally damaged and computer doesn't boot from it, I boot from USB stick, fire up FSArchiver, and restore A, B, C, D partitions from the external disk.

SystemRescueCD with FSArchiver is an excellent disaster recovery tool.