By virtue of the advanced numerical techniques and in-situ measurements, it is now possible to develop suitable methodologies to be used in the decision making on the rehabilitation of the historical and monumental structures. In this sense, this article presents suitable approaches to support decision-making process. Discrete- and continuum-based finite element modeling strategies that are to be used in the seismic assessment of masonry structures are investigated. The calibration of finite element models by the use of available experimental data is also introduced. In the calibration of discrete models, a finite element model updating (FEMU) procedure that considers the stiffness of contact between adjacent stone units was used. The time history seismic analysis of the updated models were finally carried out using both implicit and explicit time integration schemes in order to introduce the differences in the prospective modelling approaches. First, adopted strategy was verified on a simulated column. Thereafter, a contemporary masonry monument and a historical tower were used to demonstrate the methodologies using experimental data. Some modeling tips for general purpose FE softwares are also given.