We consider a calculus for multiparty sessions enriched with security levels for messages. We propose a monitored semantics for this calculus, which blocks the execution of processes as soon as they attempt to leak information. We illustrate the use of this semantics with various examples, and show that the induced safety property is compositional and that it is strictly included between a typability property and a security property proposed for an extended calculus in previous work. † Dedicated to the Memory of Kohei Honda