This article aims to present the results of the investigations performed on a 19th-century oil painting on canvas belonging to the Conservation and Restoration Department of the University of Art and Design in Cluj-Napoca, Romania. The artwork depicting the portrait of a lady originating from an important Irish noble family (Judith Bunbury, 1785–1861) has been investigated using only non-invasive methods. The investigation protocol included digital photography in different light sources at different wavelengths, which was used to document the current condition of the painting, UV fluorescence, which highlighted the previous improper retouches and the presence of a varnish coat, Infrared reflectography, which brought to light the underdrawing made by the artist and X-ray Fluorescence (XRF) spectroscopy, an elemental analysis technique which indicated the chemical composition of the pigments, suggesting the use of lead white, a barium white pigment, yellow and red ochre, vermilion, cobalt blue, and a manganese-based brown pigment. The results of this entirely non-invasive investigation approach helped in choosing the most appropriate conservation and restoration methodology for the artwork.