The durability of sandstones of historical building materials and geoheritage landforms is a major issue that requires an assessment methodology to follow salt weathering evolution. The building blocks of monuments support decorative carvings and reliefs that are outstanding testimonies of human activity. An evaluation based on quasi- and non-destructive testing is a reliable and generally accepted way of testing and inspecting historical building materials. Compression tests were performed on specimens of similar building sandstones extracted close to those of from St. Leonard’s Middle Ages Church, and microdrilling tests were carried out on adequate blocks of this monument. The locations of the latter tests were determined using the results of low-pressure water absorption tests, which contributed to finding a link between the sandstone specimens and the building blocks of the monument. This innovative methodology was used to generate simulated stress–strain diagrams of the building blocks of this church based on drilling strength results, avoiding the cutting of specimens from the façades with the sizes needed to ensure the mechanical validity of the results. A good agreement between the predicted and experimental stress–strain curves was achieved. The stress–strain curves of sound stones from historical building blocks and of their weathered envelopes are shown. The evolution of weathering profiles can be followed through the analysis of stress–strain diagrams, allowing an assessment of structural stability, which is essential to the study of the durability of historical building sandstones. This innovative methodology allows the adequate conservation of monuments and is a contribution to the knowledge of sustainable cultural tourism.