The interferometry-based experimental tests of quantum properties of space-time which the author sketched out in a recent short paper are here discussed in a self-contained fashion. In addition to providing detailed derivations of the results already announced in the previous paper, some new results an also derived; in particular, the analysis is extended to a larger class of scenarios for space-time fuzziness. It is argued that these studies could be helpful for the search for a theory describing a first stage of partial unification of gravity and quantum mechanics.