Cosmic-ray exposure dating of preserved, seismically exhumed limestone normal fault scarps has been used to identify the last few major earthquakes on seismogenic faults and recover their ages and displacements through the modelling of the content of in situ [36Cl] cosmonuclide of the scarp rocks. However, previous studies neglected some parameters that contribute to 36Cl accumulation and the uncertainties on the inferred earthquake parameters were not discussed. To better constrain earthquake parameters and to explore the limits of this palaeoseismological method, we developed a Matlab® modelling code (provided in Supplementary information) that includes all the factors that may affect [36Cl] observed in seismically exhumed limestone fault scarp rocks. Through a series of synthetic profiles, we examine the effects of each factor on the resulting [36Cl], and quantify the uncertainties related to the variability of those factors. Those most affecting the concentrations are rock composition, site location, shielding resulting from the geometry of the fault scarp and associated colluvium, and scarp denudation. In addition, 36Cl production mechanisms and rates are still being refined, but the importance of these epistemic uncertainties is difficult to assess. We then examine how pre-exposure and exposure histories of fault-zone materials are expressed in [36Cl] profiles. We show that the 36Cl approach allows unambiguous discrimination of sporadic slip versus continuous creep on these faults. It allows identification of the large slip events that have contributed to the scarp exhumation, and provides their displacement with an uncertainty of +/- ~25 cm and their age with an uncertainty of +/-0.5-1.0 kyr. By contrast, the modelling cannot discriminate whether a slip event is a single event or is composed of multiple events made of temporally clustered smaller size events. As a result, the number of earthquakes identified is always a minimum, while the estimated displacements are maximum bounds and the ages the approximate times when a large earthquake or a cluster of smaller earthquakes have occurred. We applied our approach to a data set available on the Magnola normal fault, Central Italy, including new samples from the buried part of the scarp. Reprocessing of the data helps to refine the seismic history of the fault and quantify the uncertainties in the number of earthquakes, their ages and displacements. We find that the Magnola fault has ruptured during at least five large earthquakes or earthquake clusters in the last 7 ka, and may presently be in a phase of intense activity.