You can get a very powerful sword for Steiner by completing a short side quest. Return to Daguerreo on Disc 4. An old man near the Library's Inn asks you to look out for an item called the Magical Fingertip. Go to the Treno Auction and bid on this item. You may have to pay somewhere around 85,000 Gil in the bidding war, so make sure it's worth it to you.
If you don't see the Magical Fingertip at the Auction House, then you may need to sell all of the Key Items you purchased at the Auction previously, such as the Doga's Artifact, Rat Tail, Griffin's Heart, and Une's Mirror. This should make the Magical Fingertip available at the Auction House. In addition, you should be able to repurchase the items you had to sell.
Take the Magical Fingertip back to the old man in Daguerreo. When you give him the item, he tells you his life's story and then gives you Excalibur. This sword, which is not as powerful as the Ragnarok found during the "Chocobo Hot and Cold" game, enables Steiner to learn Climhazzard.
To get Excalibur II you'll have to reach the Terrace in Memoria within 12 game hours. You can find the Excalibur II on the Terrace to your right. This is the most powerfull weapon in the game!