  We formulate off-shell N=1 superconformal higher spin multiplets in four
spacetime dimensions and briefly discuss their coupling to conformal
supergravity. As an example, we explicitly work out the coupling of the
superconformal gravitino multiplet to conformal supergravity. The corresponding
action is super-Weyl invariant for arbitrary supergravity backgrounds. However,
it is gauge invariant only if the supersymmetric Bach tensor vanishes. This is
similar to linearised conformal supergravity in curved background.
