The common beamline of the AWAKE experiment at CERN involves the co-propagation of two particle beams: protons with 48 nC bunch charge and 250 ps bunch length, and electrons with up to 600 pC bunch charge and approximately 4 ps bunch length. The existing operational beam position monitors at AWAKE cannot measure the electron bunches whilst the more-intense proton bunches are present, due to their low operating frequency. In order to try to address this challenge, two different types of high-frequency pick-ups were studied, a conical-shaped button pick-up and a Cherenkov diffraction radiation-based pick-up designed to operate at around 30 GHz. Both devices were installed at AWAKE and were connected to two identical read-out systems designed by TRIUMF. This contribution presents and discusses the results obtained from beam-based measurements during the current experimental year.