Comment 2 for bug 145750

Swap partition has to be at least 100mb larger than amount of RAM.
If so and hibernate still doesn't work, try the following:

(replace your swap partition dev_name for hdXX, for example hda8 - check with "cat /etc/mtab")

sudo mkswap -L UBUNTU_SWAP /dev/hdXX

sudo vol_id /dev/hdXX
or
sudo blkid
You will get UUID for your swap partition, for example mine is: 4befafea-ff8a-4ac8-b727-dc38e0d4f4dc

Then edit /etc/initramfs-tools/conf.d/resume
RESUME=UUID=place_here_uuid_for_hdXX

You can place "/dev/hdXX" instead of "UUID=uuid_for_hdXX" but it's rather obsolete habit

sudo update-initramfs -k all -u

reboot and then try to hibernate