Objective. Ionization chambers, mostly used for beam calibration and for reference dosimetry, can show high recombination effects in pulsed high dose rate proton beams. The aims of this paper are: first, to characterize the linearity response of newly designed asymmetrical beam monitor chambers (ABMC) in a 100-226 MeV pulsed high dose rate per pulse scanned proton beam; and secondly, to calibrate the ABMC with a PPC05 (IBA Dosimetry) plane parallel ionization chamber and compare to calibration with a home-made Faraday cup (FC). Approach. The ABMC response linearity was evaluated with both the FC and a PTW 60019 microDiamond detector. Regarding ionometry-based ABMC calibration, recombination factors were evaluated theoretically, then numerically, and finally experimentally measured in water for a plane parallel ionization chamber PPC05 (IBA Dosimetry) through k _s saturation curves. Finally, ABMC calibration was also achieved with FC and compared to the ionometry method for 7 energies. Main results. Linearity measurements showed that recombination losses in the new ABMC design were well taken into account for the whole range of the machine dose rates. The two-voltage-method was not suitable for recombination correction, but Jaffé’s plots analysis was needed, emphasizing the current IAEA TRS-398 reference protocol limitations. Concerning ABMC calibration, FC based absorbed dose estimation and PPC05-based absorbed dose estimation differ by less than 6.3% for the investigated energies. Significance. So far, no update on reference dosimetry protocols is available to estimate the absorbed dose in ionization chambers for clinical high dose rate per pulse pulsed scanned proton beams. This work proposes a validation of the new ABMC design, a method to take into account the recombination effect for ionometry-based ABMC calibration and a comparison with FC dose estimation in this type of proton beams.