How did Frodo get his Mithril Coat back?

[Inziladun]

Originally Posted by William Cloud Hicklin

One also suspects, although this is nowhere stated, that had Sauron recovered the Ring Gandalf, as the bearer of Narya, would have been aware of it - just as the original bearers of the Three were aware of the One the moment Sauron completed it.

If that were the case though, what would account for Gandalf's obvious anxiety when he learned from Faramir that Frodo had headed for Cirith Ungol, and apparently equated the darkness from Mordor with Frodo's capture?

Pippin became aware that Gandalf's hands were trembling....with a thrill of fear Pippin knew that Gandalf, Gandalf himself, was troubled, even afraid.

Faramir gleaned the source of Gandalf's worry.

'Indeed I see what you fear. But the darkness is not due to [Frodo and Sam's] venture....It is clear to me that the Enemy has long planned an assault on us, and [the darkness's] hour had already been determined before ever the travellers left my keeping.'

ROTK The Siege of Gondor

If Gandalf thought Narya would be an indicator that Sauron had regained the One, I see no reason he would have associated the darkness with Frodo's intended destination.