After compiling and installing a newer kernel version, I don't really backup my old kernel, instead I keep the image and the modules until I make sure the new one works as I want it to.
Anyway, the files you may want to backup is /boot/vmlinuz-version, /boot/System.map-version, /boot/initrd-version (if case) and the modules found at /lib/modules/version, where version is something like 2.4.27-2.
PS: Is it possible to set up grub to boot from different kernels? For example, adding a entry for the new kernel and keeping the old entry?
Of course, after you install the modules (make modules_install), copy the new vmlinuz and the new System.map to /boot, edit menu.lst to look something like:
title Debian GNU/Linux, kernel 2.4.27-2-386
kernel /boot/vmlinuz-2.4.27-2-386 root=/dev/hda2 ro
title Debian GNU/Linux, kernel 188.8.131.52
kernel /boot/vmlinuz-184.108.40.206 root=/dev/hda2 ro
This way you keep both kernels. Once you think you don't need the old kernel, remove the old files from /boot and the corresponding directory in /lib/modules.
On a side note, you could compile your new kernel without the need of an initrd.