Ab initio studies reveal the interplay between structure and quantum effects in atomic-sized Cu nanocontacts. Our approach is based on density functional theory within the frame of a Korringa-Kohn-Rostoker Green's function method. We present evidence that the electronic structure of nanocontacts during stretching is governed by quantum-mechanical resonances. Our results indicate that the quantum size-effects have a profound effect on electronic states of contacts before breaking.