  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 $\sim$10 m s$^{-1}$ precision over the entire
optical wavelength range on scales of both echelle orders ($\sim$50--100 \AA)
and entire spectrographs arms ($\sim$1000--3000 \AA). Using archival spectra
from the past 20 years we have probed the supercalibration history of the
VLT--UVES and Keck--HIRES spectrographs. We find that systematic errors in
their wavelength scales are ubiquitous and substantial, with long-range
distortions varying between typically $\pm$200 m s$^{-1}$ per 1000 \AA. 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,
$\alpha$. The spurious deviations in $\alpha$ 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 $\alpha$ from quasar absorption lines.
