Discrete image-potential state (IS) resonances at Co nanoislands on Au(111) are probed using scanning tunneling microscopy and spectroscopy. We observe particle-in-box-type standing wave patterns, which is surprising in view of the high energy of the IS electrons when compared to the confining potential imposed by the island edges. The weak confining potential experienced by the IS electrons results in electronic interaction effects between closely spaced islands. Probing high-energy ISs hence provides a novel route to investigate electronic coupling between nanoislands on surfaces.