The field of self-testing focuses on understanding the structure of quantum bipartite correlations and identifying those correlations that admit a unique physical realization up to local isometries. Apart from its applications in Quantum Information Theory, self-testing has been a key ingredient in results related to quantum complexity theory and the resolution of Connes’ embedding problem, which motivated the study of self-testing in an operator algebraic context. This direction was recently explored by Padock, Slofstra, Zhao, and Zhou, who introduced abstract self-testing of quantum correlations as a unique extension property of a state on the tensor product of associated operator systems to the corresponding tensor product of C*-algebras. Building on their work, we developed a general framework for self-testing in the context of general operator systems. As an application of this abstract approach, we define and examine self-testing for recently introduced classes of quantum no-signalling correlations. Alongside the abstract notion of self-testing, we propose an operational approach by defining local isometries in this broader context, which is novel even for classical no-signalling quantum commuting correlations. This talk is based on joint work with Jason Crann and Ivan G. Todorov.