  We present a detailed analysis of a very high resolution (R\approx 112,000)
spectrum of the quasar HE 0515-4414 obtained using the High Accuracy Radial
velocity Planet Searcher (HARPS) mounted on the ESO 3.6 m telescope at the La
Silla observatory. The HARPS spectrum, of very high wavelength calibration
accuracy (better than 1 m\AA), is used to search for possible systematic
inaccuracies in the wavelength calibration of the UV Echelle Spectrograph
(UVES) mounted on the ESO Very Large Telescope (VLT). We have carried out
cross-correlation analysis between the Th-Ar lamp spectra obtained with HARPS
and UVES. The shift between the two spectra has a dispersion around zero of
\sigma\simeq 1 m\AA. This is well within the wavelength calibration accuracy of
UVES (i.e \sigma\simeq 4 m\AA). We show that the uncertainties in the
wavelength calibration induce an error of about, \Delta\alpha/\alpha\le
10^{-6}, in the determination of the variation of the fine-structure constant.
Thus, the results of non-evolving \Delta\alpha/\alpha reported in the
literature based on UVES/VLT data should not be heavily influenced by problems
related to wavelength calibration uncertainties. Our higher resolution spectrum
of the z_{abs}=1.1508 damped Lyman-\alpha system toward HE 0515-4414 reveals
more components compared to the UVES spectrum. Using the Voigt profile
decomposition that simultaneously fits the high resolution HARPS data and the
higher signal-to-noise ratio UVES data, we obtain,
\Delta\alpha/\alpha=(0.05\pm0.24)x10^{-5} at z_{abs}=1.1508. This result is
consistent with the earlier measurement for this system using the UVES spectrum
alone.
