  Tunnelling between non-centrosymmetric superconductors with significant
spin-orbit splitting is studied theoretically in a two-band treatment of the
problem. We find that the critical Josephson current may be modulated by
changing the relative angle between the vectors describing absence of inversion
symmetry on each side of the junction. The presence of two gaps also results in
multiple steps in the quasiparticle current-voltage characteristics. We argue
that both these effects may help to determine the pairing states in materials
like CePt$_3$Si, UIr and Cd$_2$Re$_2$O$_7$. We propose experimental tests of
these ideas, including scanning tunnelling microscopy.
