Montague is a Sensate and can be found in the Civic Festhall in the Clerk's Ward. He is romantically involved with Juliette, one of the prostitutes at the Brothel for Slaking Intellectual Lusts.
Juliette will tell TNO, as part of the Nine students quest, that her romance with Montague lacks excitement. Towards the end of resolving this issue, TNO can propose a forged Love Letter to make Montague jealous. This can be procured from Scofflaw Penn at the Print Shop or by stealing one from Yves' room. Sharing this letter with Montague and tipping him off about it's true nature should add some spice to the romance (as well as award 5000 XP). Likewise, encouraging Montague to perform a ruse himself against Juliette will also provide spice to the romance (and 5000 XP)