By means of ion bombardment of clean Au(111) films, atomically flat nanoparticles of various shapes and sizes were created, ranging from several tens of nm(2) down to only a few nm(2). Both two-dimensional Au islands as well as one-dimensional Au nanowire-like structures have been investigated by means of low-temperature scanning tunneling microscopy and spectroscopy. We were able to probe their local electronic structure in a broad energy range, which was found to be dominated by pronounced size-dependent confinement effects. Mapping of the local density of states revealed complex standing wave patterns that arise due to interference of scattered Au surface state electrons at the edges of the Au nanoparticles. The observed phenomena could be modeled with high accuracy by theoretical particle-in-a-box calculations based on a variational method that can be applied to '2D boxes' of arbitrary polygonal shape and that we have previously successfully applied to explain the electronic wave patterns on Co islands on Au(111). Our findings support the general validity of this particle-in-a-box model.