The adjective “experimental” appears odd when applied to astronomy, which is a discipline based on observations at a distance. Nevertheless, during the last 40 years the traditional “History of astronomy” generated two additional branches: the so-called “Experimental history of astronomy” and “Experimental historical astronomy”. The first branch aims at verifying old astronomical data and theories by performing new observations. The second branch has as its purpose the elaboration or the confirmation of new astronomical theories via the examination of ancient observational records. In this paper, beside a brief examination of both branches, I will introduce two examples based upon the repetition of observations with ancient monumental meridian lines in the city of Florence, Italy: the one in the church of Santa Maria del Fiore, dating back to epoch of Paolo dal Pozzo Toscanelli, and the one in the Storks’ Room of the Torrino of the Specola, built in the fourth quarter of the eighteen century. In addition to singling out the sound observational bases of the (optical) theories of Egnatio Danti, and providing evidence which confirm modern planetary phenomena, as the variation of the obliquity of the ecliptic, such large meridian lines are also useful in ascertaining the stability and the structural alterations of the historical buildings.