A method for operating a scanning probe microscope at elevated scan frequencies has a characterization stage of sweeping a plurality of excitation frequencies of the vertical displacement of the scanning element; measuring the value attained by the reading parameter at the excitation frequencies; and identifying plateau regions of the response spectrum of the reading parameter. The reading parameter variation is limited within a predetermined range over a predefined frequency interval, thereby defining corresponding fast scanning frequency windows in which the microscope assembly is sufficiently stable to yield a lateral resolution comparable to the one obtained during slow measurements. The measurement stage includes driving the scanning element along at least a scanning trajectory over the surface of the specimen at a frequency selected among the frequencies included in a fast scanning frequency window.