The structures of the doubly ordered perovskites NaCeMnWO6 and NaPrMnWO6, with rock salt ordering of the Mn2+ and W6+ B-site cations and layered ordering of the Na+ and (Ce3+/Pr3+) A-site cations, have been studied by transmission electron microscopy, electron diffraction, neutron and synchrotron X-ray powder diffraction. Both compounds possess incommensurately modulated crystal structures. In NaCeMnWO6 the modulation vector (with reference to the ideal ABX(3) perovskite subcell) is q approximate to 0.067a* (similar to 58.7 angstrom) and in NaPrMnWO6 q approximate to 0.046a* (similar to 85.3 angstrom). In both compounds the superstructures are primarily the two-dimensional chessboard type, although some crystals of NaCeMnWO6 were found with one-dimensional stripes. In some crystals of NaPrMnWO6 there is a coexistence of chessboards and stripes. Modeling of neutron diffraction data shows that octahedral tilting plays an important role in the structural modulation.