Cosmic radiation exposure of aircraft crew, which is generally evaluated by numerical simulations, should be verified by measurements. From the perspective of radiological protection, the most contributing radiation component at aviation altitude is neutrons. Measurements of cosmic neutrons, however, are difficult in a civilian aircraft because of the limitations of space and electricity; a small, battery-operated dosimeter is required whereas larger-size instruments are generally used to detect neutrons with a broad range of energy. We thus examined the applicability of relatively new transportable neutron monitors for use in an aircraft. They are (1) a conventional rem meter with a polyethylene moderator (NCN1), (2) an extended energy-range rem meter with a tungsten-powder mixed moderator (WENDI-II), and (3) a recoil-proton scintillation rem meter (PRESCILA). These monitors were installed onto the racks of a business jet aircraft that flew two times near Japan. Observed data were compared to model calculations using a PHITS-based Analytical Radiation Model in the Atmosphere (PARMA). Excellent agreement between measured and calculated values was found for the WENDI-II. The NCN1 showed approximately half of predicted values, which were lower than those expected from its response function. The observations made with PRESCILA showed much higher than expected values; which is attributable to the presence of cosmic-ray protons and muons. These results indicate that careful attention must be paid to the dosimetric properties of a detector employed for verification of cosmic neutron dose.