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In regions with low-to-moderate seismicity, the return-period of seismic events with large magnitudes is relatively high. Nevertheless, historical seismic events are relevant for the evaluation of seismic hazard in those regions. Thus, seismologists study the records of the effects of historical earthquakes to map the distribution intensity points, using an Intensity Scale. Afterwards, the maximum intensity point is identified as well as the probable epicentral location and magnitude. Another method, introduced by earthquake engineers, incorporates the knowledge of the behaviour of structures into posterior distributions of magnitude using fragility functions and the damage reported in historical documents. The method uses the total probability theorem to combine the uncertainty in the structural behaviour, ground motion intensity, site-to-source distance. Then, the Bayes’s theorem is employed to update a prior magnitude model into a posterior magnitude distribution. Thus, the reduction of the uncertainty in the final estimates requires the preliminary application of the method to instrumental events in order to validate the appropriate framework to address historical seismicity, namely ground motion and structural response. This paper investigates the earthquakes of January 1st 1980 with Mw=6.8-7.2 and of July 9th 1998 with Mw=5.9-6.2 in Azores Islands (Portugal) as study cases to test the sensitivity to different attenuation models Ambraseys et al. (2005) and Akkar et al. (2014). A single set of fragility functions, derived from a detailed vulnerability assessment in Faial, is assumed to model the structural response in both events. The results show that, for both events, the attenuation model from Akkar et al. (2014) and the fault source model presented results closer to those of detailed methods. Discrepancies can also be explained by differences in the prior distance model resulting from source models assumptions. The intervals Mw=5.96±0.53 and Mw=6.91±0.42 have been estimated for the 1998 and the 1980 earthquake, respectively. info:eu-repo/semantics/publishedVersion