Each character has his or her own Celestial Weapon, but in order to get the character Celestial Weapon you must have the Celestial Mirror. The weapons have an advantage, which allows them to penetrate any amour and has one disadvantage no AP ability. You will need a Crest and Sigil to remove the no AP ability. If you use one of the Crest or Sigil you will activate the Double Overdrive Ability but still have the no AP ability. To remove the no AP ability you must have both the Crest and Sigil.
Below is a list of each character Celestial Weapons.
-»Tidus - Caladbolg-»Yuna - Nirvana
-»Auron - Masamune
-»Wakka - World Champion
-»Kimahri - Spirit Lance
-»Lulu - Onion Knight
-»Rikku - Godhand