The absolute dating of mortar by accelerator mass spectrometry (AMS) has been the subject of renewed interest for several years. International intercomparison campaigns, called MODIS (MOrtar Dating Intercomparison Study), have been carried out. The first MODIS-1 campaign highlighted limitations in mortar dating, due to the similarity between the primary material to be dated (binder) and the contaminant (exogenous CaCO3). Methods have since emerged to overcome this problem and the need for a good preliminary characterization has been proven. The Laboratoire de Mesure du Carbone 14 (LMC14) took part in the second intercomparison campaign, MODIS2, by applying thermal decomposition increments to distinguish the carbonated binder, the organic matter contaminants (late in formation pyrogenic carbonate, LDH) and limestone. The LMC14 results on MODIS2 are quite conclusive on “pure” re-carbonated lime mortar binders containing little contaminant geological limestone but show their weaknesses for mortars heavily contaminated in Dolomites, which are difficult to discern from the binder. Recommendations for users of radiocarbon (14C) dating on mortar-based materials are made in the conclusion.