Electron confinement in hexagonal vacancy islands on Cu(111) is studied by state of the art ab initio calculations and experimentally by low-temperature scanning tunneling spectroscopy measurements (STS). Both theory and experiment reveal standing wave patterns of the local density of states (LDOS), which are ascribed to the scattering of surface-state electrons at the boundary of the vacancy island. The spatial modulation of the LDOS, its size, and energy dependence as measured by STS are well reproduced by our calculations. This agreement between theory and experiment corroborates the application of our theoretical approach to other confined systems, including spin-polarized effects. Our studies predict that quantum states of vacancy islands with magnetic adatoms can be used to tailor the spin-polarization of surface-state electrons on metal surfaces.