Queen Cersei eyes Kirth coldly. "You were observed conspiring with the Ned Stark before his imprisonment. Time in the dungeons will reveal your true loyalties."
Ask where King Joffrey is.
Demand to speak to the King.
Submit willingly to Queen Cersei's decision.
Argue that the pledge of House [Your Name] is an answer to her concerns.
"None of your concern. Many Baratheons traipse about, pleding loyalty. Until I'm satisfied House [Your Name] isn't traitorous, you'll rot in a cell."