MethaneSAT was a push-broom, area-mapping satellite that quantified area and point source methane (CH₄) emissions across global target areas. Two sensors onboard MethaneSAT measured short-wave infrared absorption bands of CH₄, carbon dioxide, and oxygen. We report novel methods for MethaneSAT spectral calibration during pre-launch measurements and on-orbit operation. We derive and compare instrument spectral response functions (ISRFs) measured during ground calibrations at the individual sensor level at three temperatures and at the integrated flight system level. Point spread functions are used to develop peak and ghost stray-light kernels. Underlying line shape exposures were stray-light corrected based on these kernels prior to deriving ISRFs. Novel methods robustly merge ISRFs at three overlapping slit illumination fields of view and identify bad ISRF positions for gap filling. We evaluate four distinct ISRF data sets for on-orbit calibration across three different thermal conditions by squeezing the ISRF in level 2 (L2) retrievals. ISRF widths varied by <5% between calibration experiments across a wider range of thermal environments than those observed on-orbit. The use of ISRFs measured at temperatures closest to those observed on-orbit resulted in a value close to unity for the parameter that squeezes the ground-based calibration derived ISRFs in L2 retrievals. A time series of these squeeze factor deviations demonstrate relatively stable on-orbit spectral calibration across the mission duration with <0.4% variations. Our results demonstrate stable on-orbit instrument spectral response and on-orbit wavelength shift variations compared with ground-based calibration across expected on-orbit thermal conditions. These results support the high accuracy and stability of MethaneSAT L2 retrievals.