The correct specification of spatial models, and especially the choice of the spatial weights matrix, represents a crucial decision for researchers using georeferenced data. However, few guidelines exist on which weights matrix is most appropriate in certain cases. This paper therefore (1) studies the sensitivity of testing and estimating spatial models with different weights matrix specifications and (2) formulates recommendations for researchers applying spatial models regarding model selection and weights matrix specification. The research is based on Monte Carlo simulations with synthetic data.