I got intrigued and did a Google search... the poem is taken from The Tempest, Act III, Scene 1; it's spoken by Ferdinand to Miranda. Incidentally, a couple of definitions for the name "Miranda" claim that Shakespeare invented the name for this play; it's taken from the Latin word "miror" meaning, "to admire"; "Miranda" then meaning "something admirable" or "worthy of admiration". The phrase "Admirable Miranda" then becomes a play on words!
For a LOTR reference, check out this site.