Kashiwara's equivalence, saying that the category of D-modules on a variety X supported on a smooth, closed subvariety Y is equivalent to the category of D-modules on Y, is a key result in the theory of D-modules. In this talk I will explain how one can generalize Kashiwara's result to modules for deformation-quantization algebras on a conic symplectic manifold. As an illustrative application, one can use this result to calculate the additive invariants such as the K-theory and Hochschild homology of these module categories. This is based on joint work C. Dodd, K. McGerty and T. Nevins.