Cat's been in prison before. Antimagic prison cells, even, once or twice. It's part of the business. They get each other out. She spends the first while examining the cell. If she could put enough solid material between her and the emitter for the antimagic field that'd do it, but where to get the solid material from. The cell is stone, not dirt. She checks carefully that the antimagic reaches every reach of the cell, which it does, and when the guards come in she tries flirtation, bribery, appeals to their desire to make Good which is frankly unlikely as a prison guard, and whatever else strikes her. They're scared of the Queen, and don't go for it. So it goes.
(Cat's not really scared of the Queen. Cat's impression of the Queen is that she's a dick but she did close the ports and she did free Cheliax from Hell so probably she'll just yell at Andira and then let them go in exchange for some favors.)
Then they throw someone else in her cell. Unconscious. She concernedly attempts first aid.