You can use the wrong fandom trick. On the nominations form, you put in any random fandom name - Harry Potter or something - and then enter the characters you want to check.
If those characters have been nominated by someone else, you will get an error message that tells you "the character 'Dominuura (Simoun)' has already been nominated for the fandom 'Simoun', try disambiguating and submitting again".
If you don't get a hit that way, you sometimes want to try checking different variations on a character name, just in case someone entered it differently. So 'Dominuura', or 'Dominuura (Simoun)' or if there are various spellings. Like Aaeru vs. Aeru (neither of which appear to have been nommed, unfortunately).
Re: Yuletide!
If those characters have been nominated by someone else, you will get an error message that tells you "the character 'Dominuura (Simoun)' has already been nominated for the fandom 'Simoun', try disambiguating and submitting again".
If you don't get a hit that way, you sometimes want to try checking different variations on a character name, just in case someone entered it differently. So 'Dominuura', or 'Dominuura (Simoun)' or if there are various spellings. Like Aaeru vs. Aeru (neither of which appear to have been nommed, unfortunately).