  We propose a superspace formulation of N=(1,0) conformal supergravity in six
dimensions. The corresponding superspace constraints are invariant under
super-Weyl transformations generated by a real scalar parameter. The known
variant Weyl super-multiplet is recovered by coupling the geometry to a
super-3-form tensor multiplet. Isotwistor variables are introduced and used to
define projective superfields. We formulate a locally supersymmetric and
super-Weyl invariant action principle in projective superspace. Some families
of dynamical supergravity-matter systems are presented.
