A method for operating an apparatus which has an oscillatable unit. The oscillatable unit is excited to oscillate by means of a first frequency sweep within a predetermined frequency band with successive, discrete exciter frequencies of increasing or decreasing frequency. A first exciter frequency is ascertained, in the case of which, during the first frequency sweep, at least one predeterminable criterion is fulfilled. The oscillatable unit is excited by means of a second frequency sweep, wherein the frequency band, compared with the first frequency sweep, is run through in the opposite direction. A second exciter frequency is ascertained, in the case of which, during the second frequency sweep, the at least one predeterminable criterion is fulfilled. From the first exciter frequency and the second exciter frequency, via formation of an average, a measuring frequency for determining and/or monitoring at least one process variable is determined.