Using a unique momentum microscope, we measured energy-resolved momentum distributions of valence-band electrons photoemitted into the whole half-space above the Cu(111) and Cu(001) surfaces. The experimental results are compared to one-step photoemission calculations. Convincing agreement between theoretical and experimental photoelectron momentum patterns can only be achieved by orbital-dependent corrections which emulate many-body self-energy effects in the electronic structure of Cu (Strocov etal 2002 Phys. Rev. B 66 195104). By the analysis of the Shockley surface state of Cu(111), we show that these self-energy corrections also affect the surface electronic structure in specific ways.We find that the Shockley surface state of Cu(111) is shifted differently in energy than the bulk states. As a consequence, the agreement between the theoretically calculated and the experimentally measured binding energy of this surface state is improved. Energy-resolved two-dimensional valence-band photoelectron mapping provides an alternative means of determining self-energy values experimentally.