Relative symplectic cohomology, an invariant of subsets in a symplectic manifold, was recently introduced by Varolgunes. In this talk, I will present a generalization of this invariant to pairs of subsets, which shares similar properties with the singular cohomology of pairs, such as excision and a product structure. Using this new invariant, I will demonstrate new symplectic rigidity phenomena. Joint with Yaniv Ganor, Leonid Polterovich and Frol Zapolsky.