Again, whilst this is an essential scene in the novel, it isn't in the film. Why? Because of the way the novel is structured, versus the film. The last time we heard from Frodo, he'd just been captured by the orcs following the battle with Shelob. Then we feel real despair, as they show the mithril shirt to Gandalf et al, and it looks like Frodo is dead and Sauron has the Ring. In the book, it's a brilliant "all is lost" moment.

In the film, because Jackson cross cuts between Aragorn, Gandalf, etc and Frodo and Sam, we already know they escaped and are making their way up Mount Doom. So the scene becomes dramatically redundant (not to mention the bit when Aragorn cuts the Mouth of Sauron's head off is much more Peter Jackson than Tolkien - in the novel, he honours the temporary truce to negotiate).