Ba2CuTeO6 and Ba2NiTeO6 are compounds with structures related to that of the proposed spin liquid Ba3CuSb2O9. The space group and nature of the B-site ordering in Ba3CuSb2O9 have recently been reassigned. As Ba2CuTeO6 and Ba2NiTeO6 have been little studied and not at all by neutron diffraction, a determination of the correct space group and details of the nature of the distortions of the oxygen octahedra for both structures is vital for understanding the structural basis of their physical properties. The determination of the magnetic structures of these compounds using neutron diffraction is also essential as susceptibility measurements show evidence for non-trivial magnetic ordering. This study aims to determine the crystal and magnetic structures of these materials over the temperature range 1.5K to 830K.