Energy-dispersive X-ray fluorescence (EDXRF) with its portable capability, generally characterised by a small X-ray tube and a Si-PIN or Si-drift detector, is particularly useful to analyse works of art. A variety of works, such as paintings of all types (including frescos and illuminated manuscripts), bronzes and brasses, gold alloys, silver alloys, ceramics, porcelains and faiences, papers, ... [Show full abstract] ink, stones of all types (marbles, obsidians, etc), stamps, glass and so on can be studied using portable EDXRF equipment. In some cases, the information gathered is of paramount importance, such as to determine the pigments in a painting or the alloy composition in gold objects. The aspects that mainly characterise the EDXRF technique are its being non-invasive and quasi-bulk. These characteristics that make the technique so powerful and appealing are, on the other hand, the main sources of uncertainty in EDXRF measurements on cultural heritage. In the paper, it will be shown that this uncertainty is intrinsic of every non-invasive technique, especially when dealing with paintings. A Caravaggio canvas painting, Calling of Saint Matthew (1559 AD), and a Signorelli wooden painting, The Altarpiece of Paciano (1517 AD), are shown to address this point.