Abstract: One of the most important classes of even \(\Delta\)-matroids is the class of \(\Delta\)-matroids associated with orientable ribbon graphs, which plays a role analogous to graphic matroids among matroids. We characterize the class of strong \(\Delta\)-matroids that can be lifted to orientable ribbon-graphic \(\Delta\)-matroids. It is the \(\Delta\)-matroids associated with what we call pseudo-orientable ribbon graphs. Moreover, we present the corresponding geometric construction from pseudo-orientable ribbon graphs to orientable ribbon graphs that realizes the correspondence between strong \(\Delta\)-matroids and even \(\Delta\)-matroids.