Electron Paramagnetic Resonance (EPR) measurements of Erbium-doped 6H-SiC and wurtzite GaN samples are compared to total energy calculations based on density functional theory (DFT) in order to investigate the well-known luminescence of the intra 4f-shell transition at 1540 nm, useful in light-emitting diodes or lasers. The highly correlated f-electrons of Erbium (Er) have been treated within an LDA+U approach. We discus how pairs of an Er-ion with intrinsic defects can be responsible in GaN and SiC for relaxing the selection rules for intra 4f-shell transitions: In GaN our EPR investigation indicates the presence of a nitrogen vacancy next to the Er-ion. Through controlled generation of intrinsic defects in 6H-SiC single crystals and EPR measurements we support the corresponding model in SiC, that predicts defect pairs of an Er-ion and a neighboring carbon vacancy. In other words, low-energy irradiation seems to be a promising way to enhance the Er-luminescence desired for device applications.