This paper deals with the results of an experimental and numerical campaign aimed at characterizing the mechanical response of masonry components and panels made of limestone units kept together by weak air lime mortar joints. The selected air lime mortar, typical of ancient masonry buildings but difficult to be built-up artificially, was specifically prepared for the experimental analyses, with the aim of obtaining a laboratory compression strength of 0.25–0.50 MPa. In the first part of the paper, the performed tests concerning the strength of the units (mean compression strength of 80 MPa) and of the mortar (mean compression strength after 28 days of 0.30 MPa), are described for different curing periods. Moreover, tests of masonry triplets in shear (shear strength of 0.11 MPa for null axial forces) are shown and used in order to establish the main parameters of the Mohr–Coulomb failure criterium. Then, the calibration of a continuous numerical micro-model implemented in Kratos Multiphysics is presented. The model is used for reproducing the behavior of an unreinforced panel in shear made of the studied masonry and to appraise the effectiveness of a FRCM- (Fiber Reinforced Cementitious Matrix) based reinforcement intervention applied. The obtained results proved that FRCM allows to increase the strength of the considered masonry type by about eight times and the ductility by about thirteen times.