Sentinel-5 (S5) and its precursor (S5P) are future European satellite missions aiming at global monitoring of methane (CH₄) column-average dry air mole fractions (XCH₄). The spectrometers to be deployed onboard the satellites record spectra of sunlight backscattered from the Earth's surface and atmosphere. In particular, they exploit CH₄ absorption in the shortwave infrared spectral range around 1.65 μm (S5 only) and 2.35 μm (both S5 and S5P) wavelength. Given an accuracy goal of better than 2 % for XCH₄ to be delivered on regional scales, assessment and reduction of potential sources of systematic error such as spectroscopic uncertainties is crucial. Here, we investigate how spectroscopic errors propagate into retrieval errors on the global scale. To this end, absorption spectra of a ground-based Fourier transform spectrometer (FTS) operating at very high spectral resolution serve as estimate for the quality of the spectroscopic parameters. Feeding the FTS fitting residuals as a perturbation into a global ensemble of simulated S5- and S5P-like spectra at relatively low spectral resolution, XCH₄ retrieval errors exceed 0.6 % in large parts of the world and show systematic correlations on regional scales, calling for improved spectroscopic parameters.