Rovibronic molecular hydrogen (H$_2$) transitions at redshift $z_{rm abs} simeq 2.659$ towards the background quasar B0642$-$5038 are examined for a possible cosmological variation in the proton-to-electron mass ratio, $mu$. We utilise an archival sp
ectrum from the Very Large Telescope/Ultraviolet and Visual Echelle Spectrograph with a signal-to-noise ratio of $sim$35 per 2.5-km$,$s$^{-1}$ pixel at the observed H$_2$ wavelengths (335--410 nm). Some 111 H$_2$ transitions in the Lyman and Werner bands have been identified in the damped Lyman $alpha$ system for which a kinetic gas temperature of $sim$84 K and a molecular fraction $log f = -2.18pm0.08$ is determined. The H$_2$ absorption lines are included in a comprehensive fitting method, which allows us to extract a constraint on a variation of the proton-electron mass ratio, $Deltamu/mu$, from all transitions at once. We obtain $Deltamu/mu = (17.1 pm 4.5_{rm stat} pm3.7_{rm sys})times10^{-6}$. However, we find evidence that this measurement has been affected by wavelength miscalibration errors recently identified in UVES. A correction based on observations of objects with solar-like spectra gives a smaller $Deltamu/mu$ value and contributes to a larger systematic uncertainty: $Deltamu/mu = (12.7 pm 4.5_{rm stat} pm4.2_{rm sys})times10^{-6}$.
Observations of H2 spectra in the line-of-sight of distant quasars may reveal a variation of the proton-electron mass ratio mu=m_p/m_e at high redshift, typically for z>2. Currently four high-quality systems (Q0347-383, Q0405-443, Q0528-250 and J2123
-005) have been analyzed returning a constraint Dmu/mu < 1 x 10^{-5}. We present data and a mu-variation analysis of another system, Q2348-011 at redshift z_{abs}=2.42, delivering dmu/mu = (-1.5 pm 1.6) x 10^{-5}. In addition to observational data the status of the laboratory measurements is reviewed. The future possibilities of deriving a competitive constraint on Dmu/mu from the known high-redshift H2 absorbers is investigated, resulting in the identification of a number of potentially useful systems for detecting mu-variation.
