The process meter comprises a sensor that can be mounted in a wall of a vessel for holding or conveying a process medium, and a meter-electronics case mechanically coupled to the sensor. In operation, the electronics case is at least intermittently subjected to vibrations either generated in the sensor itself or transmitted via the sensor. To reduce amplitudes of such vibrations of the electronics case, at least one vibration absorber is affixed to a wall of the electronics case. This vibration absorber is vibrated at least intermittently in order to dissipate vibrational energy taken into the electronic case. By the suppression of such case vibrations, spurious components in the measurement signal can be reduced to the point that a significant improvement in signal-to-noise ratio is obtained.