We address the question of whether an optical vortex can be trapped in a dielectric structure with a core of a lower refractive index than the cladding--namely an antiguide. Extensive numerical simulations seem to indicate that this inverse trapping of a vortex is not possible, at least in straightforward implementations. Yet, the interaction of a vortex beam with a curved antiguide produces interesting effects, namely a small but finite displacement of the optical energy center-of-mass and the creation of a symmetrical vortex-antivortex pair on the exterior of the antiguide.