We calculate the characteristics of the “black hole shadow” for a rotating, neutral black hole in fourth-order conformal Weyl gravity. It is shown that the morphology is not significantly affected by the underlying framework, except for very large masses. Conformal gravity black hole shadows would also significantly differ from their general relativistic counterparts if the values of the main conformal gravity parameters, γ and κ, were increased by several orders of magnitude. Such increased values for γ and κ are currently ruled out by gravitational phenomenology. Therefore, it is unlikely that these differences in black hole shadows will be detected in future observations, carried out by the Event Horizon Telescope or other such experiments.