WENDI-II was designed at the Los Alamos National Laboratory (LANL) specifically as a wide-range rem meter, suitable for applications at particle accelerators, with response extension to 5 GeV. PRESCILA was also designed at LANL, mainly as a lightweight alternative to traditional rem meters, but has shown excellent response characteristics above 20 MeV. This Note summarises measurements performed over a span of 4 y to characterise the high-energy neutron response (>20 MeV) of these meters to several hundred million electron volts. High-energy quasi-monoenergetic beams utilised as part of this study were produced by the cyclotron facilities at the Université Catholique de Louvain (33 and 60 MeV) and the T. Svedberg Laboratory ( 46, 95, 143 and 173 MeV). In addition, measurements were also conducted at the Los Alamos Neutron Science Center, 800 MeV spallation neutron source, in broad energy fields with an average energy of 345 MeV. For the sake of completeness, data collected between 2.5 and 19 MeV in monoenergetic neutron fields at the German Physikalisch-Technische Bundesanstalt (PTB) facility are also included in this study.