Electron backscatter diffraction (EBSD) is a powerful characterization technique which allows the study of microstructure, grain size, and orientation as well as strain of a crystallographic sample. In addition, the technique can be used for phase analysis. A mirror-flat sample surface is required for this analysis technique and different polishing approaches have been used over the years. A commonly used approach is the focused ion beam (FIB) polishing. Unfortunately, artefacts that can be easily induced by Ga FIB polishing approaches are seldom published. This work aims to provide a better understanding of the underlying causes for artefact formation and to assess if the helium ion microscope is better suited to achieve the required mirror-flat sample surface when operating the ion source with Ne instead of He. Copper was chosen as a test material and polished using Ga and Ne ions with different ion energies as well as incident angles. The results show that crystal structure alterations and, in some instances, phase transformation of Cu to Cu₃Ga occurred when polishing with Ga ions. Polishing with high-energy Ne ions at a glancing angle maintains the crystal structure and significantly improves indexing in EBSD measurements. By milling down to a depth equaling the depth of the interaction volume, a steady-state condition of ion impurity concentration and number of induced defects is reached. The EBSD measurements and Monte Carlo simulations indicate that when this steady-state condition is reached more quickly, which can be achieved using high-energy Ne ions at a glancing incidence, then the overall damage to the specimen is reduced.