In recent years, probabilistic methods have become the main tool for the seismic assessment of built heritage structures. Nonetheless, probabilistic methods based on non-linear time history analyses face the challenge of a limited selection of recorded ground motions. This study statistically examines the minimum number of records that are necessary to provide a reasonable estimation of the “true” mean seismic demand for the case of masonry buildings. First, structural models are developed based on representative archetypes and typologies of the residential building stock in Portugal. Geometry and material properties are based on previously collected data. A three-dimensional macro-modelling approach is adopted in OpenSees to improve computational efficiency and consider In-Plane (IP) and Out-of-Plane (OOP) effects simultaneously. Earthquake selection, consistent with the European hazard, is carried out to cover the record-to-record variability. Incremental dynamic analysis (IDA) is conducted, and capacity curves are derived in which different damage states are identified. After estimating the moments of the distribution at different performance levels, the effect of the number of records on the convergence of the mean and variance is studied. Ultimately, this research seeks to provide complementary guidance in the process of ground motion selection that is often based simply on engineering experience.