During her incarceration, Misa doesn't give anything away.  She does ask her Shinigami to kill her however.  Rem refuses but does agree when she relinquishes her Death Note and thus giving up all of her memories with it.  After this happens, Light tells Rem he will try to rescue Misa.  He buries his Death Note and gives himself up on the pretense that he may subconsciously be Kira.  L agrees to lock Light up.  He also locks up Mr Yagami as well since he cannot stand his son's trials.