We use pore network modeling to study the impact of wettability and connectivity on waterflood relative permeability for a set of six carbonate samples. Four quarry samples are studied, Indiana, Portland, Guiting, and Mount Gambier, along with two subsurface samples obtained from a deep saline Middle Eastern aquifer. The pore space is imaged in three dimensions using X-ray microtomography at a resolution of a few microns. The images are segmented into pore and solid, and a topologically representative network of pores and throats is extracted from these images. We then simulate quasi-static displacement in the networks. We represent mixed-wet behavior by varying the oil-wet fraction of the pore space. The relative permeability is strongly dependent on both the wettability and the average coordination number of the network. We show that traditional measures of wettability based on the point where the relative permeability curves cross are not reliable. Good agreement is found between our calculations and measurements of relative permeability on carbonates in the literature. This work helps establish a library of benchmark samples for multiphase flow and transport computations. The implications of the results for field-scale displacement mechanisms are discussed, and the efficiency of waterflooding as an oil recovery process in carbonate reservoirs is assessed depending on the wettability and pore space connectivity.