After Frodo was captured and taken to Cirith Ungol, most of Frodo's stuff was taken away by the Orcs, including that mithril chestplate. Did he retrieve any of his belongings after the War Of The Ring?
Before the Orcs found Frodo and took him to the Tower of Cirith Ungol, Sam had been given the Phial of Galadriel by Frodo, and he took Sting and the One Ring with him after terrifying Shelob into retreat. At the later confrontation at the Black Gate, Gandalf, casting back his cloak and blinding and cowing the Mouth of Sauron with the blazing white light of his garments, took back Frodo’s Mithril shirt (a chain-mail thing, not armor-plating), Elven cloak and (Sam’s) sword. Then Mount Doom blew up thanks to Gollum, and all things were given back to Frodo at the Field of Cormallen.