Conviction Swords appear in the upper half of the second section of the Tziah Block within Tartarus, from floors 151 to 163. They will use Marakunda on the party before attacking. They may later be found in the second and third section of Caina within the Abyss of Time.
Conviction Sword appears in the 8th and 9th Paradise of Heaven within the Midnight Channel. It will buff itself with Matarukaja before attacking. After being defeated, it may drop a Perpetual Edge. Selling 6 Perpetual Edges will unlock the Basho daggers for Yosuke Hanamura in the shop.
In Golden, it appears in the same Paradises above. It may drop Sunstone for trade at Shiroku Pub.