We present a study into the capabilities of integrated and spatially resolved integral field spectroscopy of galaxies at z=2-4 with the future HARMONI spectrograph for the European Extremely Large Telescope (E-ELT) using the simulation pipeline, HSIM. We focus particularly on the instrument's capabilities in stellar absorption line integral field spectroscopy, which will allow us to study the stellar kinematics and stellar population characteristics. Such measurements for star-forming and passive galaxies around the peak star formation era will provide a critical insight into the star formation, quenching and mass assembly history of high-z, and thus present-day galaxies. First, we perform a signal-to-noise study for passive galaxies at a range of stellar masses for z=2-4, assuming different light profiles; for this population we estimate integrated stellar absorption line spectroscopy with HARMONI will be limited to galaxies with M_star > 10^10.7 solar masses. Second, we use HSIM to perform a mock observation of a typical star-forming 10^10 solar mass galaxy at z=3 generated from the high-resolution cosmological simulation NutFB. We demonstrate that the input stellar kinematics of the simulated galaxy can be accurately recovered from the integrated spectrum in a 15-hour observation, using common analysis tools. Whilst spatially resolved spectroscopy is likely to remain out of reach for this particular galaxy, we estimate HARMONI's performance limits in this regime from our findings. This study demonstrates how instrument simulators such as HSIM can be used to quantify instrument performance and study observational biases on kinematics retrieval; and shows the potential of making observational predictions from cosmological simulation output data.