Celestial weapons names:
Each Celestial weapon must be acquired by using the Celestial Mirror.

Tidus: Caladbolg
Abilities: Break 9999 damage, 3x Overdrive, Avoid Counter, Magic Counter

Race and defeat the Chocobo trainer in the Calm Lands. After winning the race, walk to the upper northwest section of the Calm Lands. The guard blocking a narrow pathway down into the gorge will have left his post, allowing you to pass. Tidus will then be able to use the Celestial Mirror to acquire Caladbolg.

Yuna: Nirvana
Abilities: Break 9999 damage, 3x Overdrive, Double AP, MP Cost 1
Aeon Effect: Allows Valefor to break 9999 damage limit.

Capture all nine types of fiends in the Calm Land region. After collecting them all, return to the monster arena owner. He will produce a treasure chest, containing the weapon.

Auron: Masamune
Abilities: Break 9999 Damage, 3x Overdrive, Preemptive Attack, Counter
Aeon Effect: Allows Yojimbo to break 9999 damage limit.

Acquire the Rusty Sword, which is found on the eastern cliff of the Cavern of the Stolen Fayth in the Calm Lands. Take the Rusty Sword to the statue of Lord Mi'ihen on the Mushroom Rock Road. Place the Rusty Sword before the statue to reveal a glyph. Touch it to reveal the Masamune's secret location.

Wakka: World Champion
Abilities: Break 9999 damage, 3x Overdrive, Double AP, Avoid Counter
Aeon effect: Allows Ifrit to break 9999 damage limit.

Talk to the bartender in Luca Cafe. If she refuses to turn it over, it is because you have been neglecting to play Blitz ball.

Kimahri: Spirit Lance
Abilities: Break 9999 damage, 3x Overdrive, Double AP, Avoid Counter
Aeon Effect: Allows Ixion to break 9999 damage limit.

Active three of the Qactuar Stones on the Thunder Plains, then find the Qactuar ghost flying just above the ground at Thunder Plains-South. Follow it to a small ruined lighting tower on the right side. Press Square to send a bolt of lightning to the tower to reveal a treasure holding the weapon.

Lulu: Onion Knight
Abilities: Break 9999 damage, 3x Overdrive, Magic Booster, MP cost 1
Aeon Effect: Allows Shiva to break 9999 damage limit.

Return to Baaj Temple and dive underwater. Swim towards the doors to the north and fight Geosgaeno. After defeating it, search the southern part of the circular underwater area and look for a treasure chest containing the weapon.

Rikku: Godhand
Abilities: Break 9999 Damage, 3x Overdrive, Double AP, Gillionaire.

Input the airship password GODHAND to open a secret location at Mushroom Rock. Move north to the end of this ravine, and use the Celestial Mirror on the symbol embedded in the rock face.

Crests and Sigils:

Sun Crest:
Go to Zanarkand Dome after Yunalesca battle. Explore the further area to find a set of stairs. Go up the stairs and take the Sun Crest from the treasure box.

Sun Sigil:
Get a time of 0:0:0 in the Chocobo race at the Calm Lands.

Moon Crest:
In Besaid, go to the beach. Go in the water and to the left will be a small shore with a treasure box. Get the treasure.

Moon Sigil:
In The Remiem Temple (must acquire all Aeons and defeat all of them).

Jupiter Crest:
Go to the shops in Luca, then go to the Besaid Aurochs locker room. Find the crest in a locker in the back right section.

Jupiter Sigil:
Keep playing League games until you get the Attack Reels, then the Status Reels. Then, play the tournament games until you get the Auroch Reels. Go back to playing the League games to get the Jupiter Sigil.

Saturn Crest:
At the columns after the Seymour battle will be a hidden treasure box.

Saturn Sigil:
Capture all of the blue butterflies in the butterfly game at Macalania Woods without touching the red butterflies.

Venus Crest:
Found in a treasure box in the Farplane at Guadosalam.

Venus Sigil:
Evade a total of 200 lightning bolts in a row in the Thunder Plains.

Mars Crest:
Mi'hen Highroad, in the south.

Mars Sigil:
Capture ten monsters of ten different species in ten different regions.

Mercury Crest:
There is a whirlpool of sand in the Sanubia Desert. It is in one of them.

Mercury Sigil:
Find all of the Cactaurs in the Cactaur mini-game. Then, look for a treasure box in the village of the Cactaur.