  We develop techniques for obtaining the mirror of Calabi-Yau supermanifolds
as super-Landau-Ginzburg theories. In some cases the dual can be equivalent to
a geometry. We apply this to some examples. In particular we show that the
mirror of the twistorial Calabi-Yau CP^{3|4} becomes equivalent to a quadric in
CP^{3|3} x CP^{3|3} as had been recently conjectured (in the limit where the
K\"ahler parameter of CP^{3|4} t -> \pm \infty). Moreover, we show using these
techniques that there is a non-trivial Z_2 symmetry for the K\"ahler parameter,
t -> -t, which exchanges the opposite helicity states. As another class of
examples, we show that the mirror of certain weighted projective (n+1|1)
superspaces is equivalent to compact Calabi-Yau hypersurfaces in weighted
projective n-space.
