I feel compelled to bring They Might Be Giants into this. They have a song called * I, Palindrome, I*, which has a palindrome of words in it:
"Son, I am able," she said, “though you scare me.”
“Watch,” said I.
“Beloved, I said watch me scare you though,” said she.
"Able am I, son."
Okay, so maybe it doesn’t make sense, but it sounds nifty in the recording.