Cochlear-implant (CI) users rely on temporal envelope modulations (TEMs) to understand speech, and clinical outcomes depend on the accuracy with which these TEMs are encoded by the electrically-stimulated neural ensembles. Non-invasive EEG measures of this encoding could help clinicians identify and disable electrodes that evoke poor neural responses so as to improve CI outcomes. However, recording EEG during CI stimulation reveals huge stimulation artifacts that are up to orders of magnitude larger than the neural response. Here we used a custom-built EEG system having an exceptionally high sample rate to accurately measure the artefact, which we then removed using linear interpolation so as to reveal the neural response during continuous electrical stimulation. In ten adult CI users, we measured the 40-Hz electrically evoked auditory steady-state response (eASSR) and electrically evoked auditory change complex (eACC) to amplitude-modulated 900-pulses-per-second pulse trains, stimulated in monopolar mode (i.e. the clinical default), and at different modulation depths. We successfully measured artifact-free 40-Hz eASSRs and eACCs. Moreover, we found that the 40-Hz eASSR, in contrast to the eACC, showed substantial responses even at shallow modulation depths. We argue that the 40-Hz eASSR is a clinically feasible objective measure to assess TEM encoding in CI users.