In the field of cultural heritage, understanding the nature of pigments and dyes is of great importance for conservation issues. Among the many natural dyes used in paintings or textiles, madder was one of the most important sources of red color at the time and was present in a wide variety of objects. However, due to extraction challenges, impurities, and high costs, a lot of information are not easily available. In this publication we designed a computational protocol able to reproduce the spectroscopic properties of two dyes, alizarin and alizarin red S. This framework allows us to compute both Ultraviolet-Visible absorption spectra and Nuclear Magnetic Resonance (NMR) with good accuracy as well as reproduce with precision the CIELAB color. We have also explored different types of interactions that impact these properties, notably the solvation effect. We found that microsolvation is sufficient to reproduce the experimental measurements made in water. The high accuracy of the computation method makes this technique particularly promising for a non-destructive study of dyes on works of art and the preservation of cultural heritage.