A procedure for obtaining limit lines for earthquake intensity attenuation is proposed. These are relationships that provide intensity values equal to or greater than actual values, as a function of the epicentral distance, with a percentile probability. They are useful in performing preliminary site selections for large industrial installations where more accurate attenuation models are not applicable due to the lack of a recorded seismic history of the surrounding area. As an example, a limit line valid for Sicily is presented; the results are easy to obtain and sufficiently reliable with respect to the examined territory.