We present the study, characterization, and calibration of the polarization modulation package (PMP) of the Imaging Magnetograph eXperiment (IMaX) instrument, a successful Stokes spectropolarimeter on board the SUNRISE balloon project within the NASA Long Duration Balloon program. IMaX was designed to measure the Stokes parameters of incoming light with a signal-to-noise ratio of at least 103, using as polarization modulators two nematic liquid-crystal variable retarders (LCVRs). An ad hoc calibration system that reproduced the optical and environmental characteristics of IMaX was designed, assembled, and aligned. The system recreates the optical beam that IMaX receives from SUNRISE with known polarization across the image plane, as well as an optical system with the same characteristics of IMaX. The system was used to calibrate the IMaX PMP in vacuum and at different temperatures, with a thermal control resembling the in-flight one. The efficiencies obtained were very high, near theoretical maximum values: the total efficiency in vacuum calibration at nominal temperature was 0.972 (1 being the theoretical maximum). The condition number of the demodulation matrix of the same calibration was 0.522 (0.577 theoretical maximum). Some inhomogeneities of the LCVRs were clear during the pixel-by-pixel calibration of the PMP, but it can be concluded that the mere information of a pixel-per-pixel calibration is sufficient to maintain high efficiencies in spite of inhomogeneities of the LCVRs.