It is known how to construct the mirror manifolds and the mirror branes for the Lagrangian branes in toric varieties (see Mirror Symmetry, D-branes and Counting Holomorphic Discs by Aganagic and Vafa for a review), but I couldn't find any discussion of mirror symmetry for non-space-filling coisotropic branes in these manifolds, while the examples of non-trivial coisotropic 5-branes in Calabi-Yau 3-folds are known (see Coisotropic Branes in Toric Calabi-Yau 3-folds by Saulina and Topological Chern-Simons/Matter Theories by Aganagic et al., for example).

Does anybody know any references on the subject?