Buttressed arches represent some of the most vulnerable elements in historical masonry buildings under seismic actions. Given their structural, architectural and often artistic importance, it is paramount to investigate effective retrofitting measures which satisfy reversibility and compatibility requirements for historical heritage. Among these, Fibre-Reinforced Mortar (FRM), characterised by enhanced ductility, has recently emerged in the scientific literature. In this paper, a numerical investigation aimed at exploring the effectiveness of this seismic retrofitting technique, when applied at intrados or extrados of various typologies of buttressed arches, is presented. An automatic tool for limit analysis is described and validated against a nonlinear Discrete Macro-Element modelling approach. This precedes an extensive parametric analysis, which has highlighted the effect of various geometrical features of the system on both collapse mechanism and maximum acceleration in the unreinforced configuration, and the high increase in seismic capacity provided by the retrofitting. This is particularly remarkable in case of local mechanism, i.e., wholly within the arch, in which case the FRM may be responsible of an overall shifting to a semi-global failure type.