A Prized Pendant is a sidequest in Star Ocean: The Divine Force that you can pick up in the Seaport Of Cotto.
If you speak to an NPC named Married Woman at the entrance of Seaport Of Cotto (inside) she will ask you to find a precious Keepsake Pendant and deliver it to her.
The Keepsake Pendant can be found in the Seaport Of Rythal on a boat. There are some crates on the top deck; smash them to obtain the Keepsake Pendant.
Return to Married Woman to claim your rewards.
Rewards: