Sapphique by Catherine Fisher is the sequel to Incarceron. It opens in the aftermath of Finn escaping from the prison and the Warden escaping into it.
Finn, who Claudia believes to be the missing crown prince, must now prove his identity, even as his memory remains spotty. To mix things up, another Giles appears, claiming to be the original. With the Queen taking his side, it's clear that civil war can't be far behind.
Meanwhile things inside of the prison are getting more dangerous for everyone involved. The prison AI wants more from its existence and has decided the best way to achieve that is to escape its physical bounds. Doing, that, though puts both the prison and the Realm at risk.
I'm breaking with the majority to say that Sapphique was more of a page turner for me than the original. Now that the big secret is out, namely what the prison is and where's it's located, there's more time to concentrate on how the worlds of the prison and Realm work (or don't).
In the extra space left by the vacated mystery is filled with glimpses of the damage done by the war the necessitated the mandated Era. Things aren't much better on the outside than they are on the inside of the prison.