Well, i can't say she completely saved herself, but when the heroine in dengeki daisy was kidnapped, she did take action herself. She used her phone to let her allies listen in on the convo between her and her kidnappers, and to communicate what actions she intended to take so they could back her up. In the end she was still "saved" by the male lead, but she was the one who decided the course, so I'd attribute her escape to teamwork. Especially since she only needed saving because she refused to let someone else die.
In.... Queens Quality I think? By the same author as dengeki daisy, the female lead is kidnapped, but she goes on a rage when she sees her captors mistreat the male lead who was captured trying to save her, and I think the male lead basically has to stop her from killing the kidnappers or something?

well I'm gonna leave a comment here hoping our heroine is strong enough to get out of that situation without Noah coming to the rescue on a white horse. This story is interesting, it´d be a shame if it ends up with the "mysterious" prince always saving the damsel in distress and they fall in love like that ( ̄へ ̄)
It made me think when she got kidnapped, have we EVER had a heroine in a shoji manga save herself? so boring