The sustainable management of urban greenery consists, among others, of the inventory, valuation, and protection of trees of monumental size. This article presents the results of the inspection of 13 large trees growing in the city of Sandomierz, located in south-eastern Poland. The examined specimens belong to five species: Norway maple (Acer platanoides L.), common ash (Fraxinus excelsior L.), white poplar (Populus alba L.), English oak (Quercus robur L.), and small-leaved lime (Tilia cordata Mill.). The health condition of the trees was assessed using acoustic and electrical tomography, as well as chlorophyll fluorescence tests. Diagnostics employing sound waves and electrical resistivity were crucial in assessing tree health. The data based on chlorophyll fluorescence confirmed the results obtained during tomographic examinations. It was an innovative combination of three non-invasive methods of examining the health condition of trees and their valuation. Economic valuation allows us to reduce to common denominator issues that are often difficult to decide due to different perspectives—expressing the economic value of trees. Calculating the value of trees allowed us to show the city’s inhabitants the value of trees that are of monumental size. Thanks to the cooperation of scientists with the city authorities, an economic plan for trees of monumental size was created, distinguished by an individualized and holistic approach to each specimen covered by the study. The database prepared has a chance to become an effective management instrument used by environmental protection authorities and a source of knowledge and education for the city’s inhabitants.