Climate change is a major concern in many areas characterized by soft soil, since it can induce substantial differential settlements to buildings and consequently cause structural damage. Unreinforced masonry buildings are particularly vulnerable to this. The resulting damage, in the form of tensile-shear cracks, is usually light but can lead to large economic losses. The development of computational models helps in anticipating and therefore mitigating these consequences. However, numerically predicting the effects of climate change on masonry structures is still a challenge as many uncertainties are involved. One of the aspects is the constitutive model to be used for describing the light damage. Often, constitutive models have been calibrated for the near-collapse state of structures. This contribution will focus on their performance for the light damage state. Among available damage modelling approaches, local smeared crack models are widely used in practice because of their relatively low computational burden. However, these models may show pathological mesh-dependency that jeopardizes the objectivity of the results. Micro brick-to-brick modelling can provide a more objective response but is characterized by a higher computational cost. In this work, both smeared crack (macro) and discrete (micro) models are studied in simulating light damage from static settlement actions in (2D) masonry walls. The non-objectivity of the numerical response of smeared crack models is highlighted and the sensitivity of precise crack width predictions with respect to the pre-assumed crack bandwidth is discussed. Next, simplified micromodelling approaches are employed and two interface material models are compared: a plasticity-based and a re-implemented damage-based model accounting for frictional effects. The numerical models are validated against experimental tests and a comparison in terms of global responses, crack patterns, crack widths and robustness of the algorithms is carried out. Moreover, the performance of the models in objectively quantifying light damage due to climate-induced settlements is discussed.