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 spectrum 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: $Deltamu/mu = (12.7 pm 4.5_{rm stat} pm4.2_{rm sys})times10^{-6}$.
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