This study investigated the influence of hearing-aid (HA) and cochlear-implant (CI) processing on consonant perception in normal-hearing (NH) listeners. Measured data were compared to predictions obtained with a speech perception model [Zaar and Dau (2017). J. Acoust. Soc. Am. 141, 1051–1064] that combines an auditory processing front end with a correlation-based template-matching back end. In terms of HA processing, effects of strong nonlinear frequency compression and impulse-noise suppression were measured in 10 NH listeners using consonant-vowel stimuli. Regarding CI processing, the consonant perception data from DiNino et al. [(2016). J. Acoust. Soc. Am. 140, 4404-4418] were considered, which were obtained with noise-vocoded vowel-consonant-vowel stimuli in 12 NH listeners. The inputs to the model were the same stimuli as were used in the corresponding experiments. The model predictions obtained for the two data sets showed a large agreement with the perceptual data both in terms of consonant recognition and confusions, demonstrating the model's sensitivity to supra-threshold effects of hearing-instrument signal processing on consonant perception. The results could be useful for the evaluation of hearing-instrument processing strategies, particularly when combined with simulations of individual hearing impairment.