Usually, I try to figure out what the kanji might be from the sounds/meaning of its composite kanji. If I still can't figure it out--and especially during karaoke--I pronounce unknown kanji as "kanji", often sounding like an idiot saying "kanji-kanji" over and over again.
I say what part of the sentence I know, then when I get to the kanji I don't know I just say "something". For example, "And then this happened...something... for 3 hours" or whatever context. 笑
And of course, there's also the choice of making up one's own story to follow the kanji that one can't read--ofen to the amusement of everyone present. Heck, I sometimes do this even with English songs :D