LIBS is one of the most promising techniques for rapid, in-situ elemental analyses of artworks. It does not require sample preparation, it is almost non destructive (micro sampling) and information both about major and trace elements could be obtained simultaneously. LIBS has been used to recognize the elements present in different archaeological materials and has been also proposed for on-line monitoring during the object cleaning by lasers. Quantitative determination of the material composition can supply useful information to restorers and help the object cataloguing. However, the analytical LIBS measurements on the archaeological materials were rarely reported, mainly due to difficulties to obtain the corresponding matrix-matched standards, required for the initial calibration. Alternatively, Calibration-Free (CF) approach could be used on some class of materials if all the major sample elements are detected and if the laser plasma preserves the material stochiometry. The latter condition is sometimes missing, as in the case of bronzes under nanosecond pulse laser ablation. We have developed a theoretical model for laser ablation of quaternary copper alloys, which allows for correction of the missing plasma stochiometry in CF approach. The model also predicts the optimal calibration for this type of material. In our recent work, we also obtained quantitative LIBS results on marbles by realizing the calibration standards starting from doped CaCO3 powders and by applying the corrections on the plasma parameters, different for the laboratory standards and marbles. Semi-quantitative LIBS results have been also obtained on multi-layered renaissance ceramics by subtraction of the contribution to plasma of each ceramic layer.