Spurious peaks in the site amplification characteristics estimated by horizontal-to-vertical spectral ratios (HVSR) of microtremors can be generated when ground motion is characterized by negligible spectral amplitudes and instrumental/numerical noise is dominant. In order to individuate HVSR maxima that cannot be safely considered as an effect of actual ground-motion characteristics, a new statistical procedure is proposed. In particular, statistics can be computed with the assumption that random noise is Gaussian. In this case, it results that the proposed statistics are independent from the level of noise and only depends on the procedures adopted for the computations of spectral amplitudes from the monitored signal. In order to use such statistics to discriminate suspect HVSR peaks, its major sampling properties in the case of signal dominated by random noise have been deduced by numerical simulations. An application of this methodology to HVSR measurements carried out at a test site in northern Italy is described and discussed.