The removal of salt from porous building materials under the influence of an applied voltage gradient normally results in high pH gradients due to the formation of protons and hydroxyl ions at the electrodes. The formed acidic and alkaline regions not only lead to disintegration of the porous material, but also affect the salt transport. In this work we use ion exchange membranes between the electrodes and the porous material to prevent the protons and hydroxyl ions from intruding into the material. The porous material used in this study is fired clay brick, which has been saturated with a 4 mol/l sodium chloride solution prior to the desalination treatment. In order to experimentally determine the salt removal, we monitored the sodium ion concentration profiles across the material with nuclear magnetic resonance (NMR). In addition, we present theoretical predictions for the salt removal according to a model based on the Poisson-Nernst-Planck theory for ion transport. From the work reported here, we can conclude that the use of ion exchange membranes to desalinate porous building materials is not useful since it reduces the salt removal rate to such an extent that desalination with poultices, which is driven by diffusion only, is more efficient. The reason behind this is twofold. First, the ion exchange membranes provide a penalty for the ions to leave the material. Second, in the absence of acidic and alkaline regions, the salt concentration at the edges of the porous material will reduce to almost zero, which leads to a locally increased electrical resistance, and thus a reduction of the electrical field in the bulk of the material. Due to this reduction the effect of the applied voltage gradient across the material vanishes, and the salt removal is limited by diffusion.