We present a new ‘supercalibration’ technique for measuring systematic distortions in the wavelength scales of high-resolution spectrographs. By comparing spectra of ‘solar twin’ stars or asteroids with a reference laboratory solar spectrum, distortions in the standard thorium–argon calibration can be tracked with ∼10 m s−1 precision over the entire optical wavelength range on scales of both echelle orders (∼50–100 Å) and entire spectrographs arms (∼1000–3000 Å). Using archival spectra from the past 20 yr, we have probed the supercalibration history of the Very Large Telescope-Ultraviolet and Visible Echelle Spectrograph (VLT-UVES) and Keck-High Resolution Echelle Spectrograph (HIRES) spectrographs. We find that systematic errors in their wavelength scales are ubiquitous and substantial, with long-range distortions varying between typically ±200 m s−1 per 1000 Å. We apply a simple model of these distortions to simulated spectra that characterize the large UVES and HIRES quasar samples which previously indicated possible evidence for cosmological variations in the fine-structure constant, α. The spurious deviations in α produced by the model closely match important aspects of the VLT-UVES quasar results at all redshifts and partially explain the HIRES results, though not self-consistently at all redshifts. That is, the apparent ubiquity, size and general characteristics of the distortions are capable of significantly weakening the evidence for variations in α from quasar absorption lines.