I recently had to repartition a disk (using parted), to resize some partitions. This meant redoing the swap partition. In my /etc/fstab, all mounts are done via UUID's, including the swap. So, poking around a bit to figure out what the UUID is/was for my new swap partition, I did the following:

root@jake 272/0 # mkswap  /dev/sda4
Setting up swapspace version 1, size = 3894268 KiB
no label, UUID=7d0f43ed-85f9-4e05-be8f-42cf12104bad
root@jake 273/0 # blkid
/dev/sda2: UUID="7b0741cd-a19a-4111-a3fe-3ed4d74706ba" TYPE="ext4"
/dev/sda3: UUID="49fac9f3-3547-420f-afc0-88dfac70459f" TYPE="ext4"
/dev/sda4: UUID="7d0f43ed-85f9-4e05-be8f-42cf12104bad" TYPE="swap"

Then it's just a matter of using the new UUID for the swap partition (/dev/sda4) in /etc/fstab, e.g.

UUID=49fac9f3-3547-420f-afc0-88dfac70459f /                       ext4    defaults        1 1
UUID=7b0741cd-a19a-4111-a3fe-3ed4d74706ba /boot                   ext4    defaults        1 2
UUID=7d0f43ed-85f9-4e05-be8f-42cf12104bad swap                    swap    defaults        0 0
tmpfs                                     /mnt/tmpfs              tmpfs   size=192m,noatime 0 0