Cross-spring pivots have been widely employed over the last decades in a broad variety of precision engineering applications due to the high motion repeatability achieved thanks to the absence of stick slip and clearance. In this paper, the non-linear effect of the anticlastic curvature of the leaf-springs is considered for the accurate analytical modeling of the elasto-kinematic behavior of cross-spring pivots. Finite element analyses (FEA), based on a non-linear thin-shell model, are carried out in order to compare them with the analytical results for the main performance parameters of this type of device, i.e. center-shift, rotational stiffness and stress in the leaf-springs. Furthermore, an experimental setup is built to assess the applicability limits of both models. Finally, remarkable performance aspects of cross-spring pivots are discussed aiming for design improvements.