Enforcement of noninterference requires proving that an attacker's knowledge about the initial state remains the same after observing a program's public output. We propose a hybrid monitoring mechanism which dynamically evaluates the knowledge that is contained in program variables. To get a precise estimate of the knowledge, the monitor statically analyses non-executed branches. We show that our knowledge-based monitor can be combined with existing dynamic monitors for non-interference. A distinguishing feature of such a combination is that the combined monitor is provably more permissive than each mechanism taken separately. We demonstrate this by proposing a knowledge-enhanced version of a no-sensitive-upgrade (NSU) monitor. The monitor and its static analysis have been formalized and proved correct within the Coq proof assistant.