The crystallization of salts is widely recognized as one of the most significant causes of irreversible damage to many cultural objects such as wall paintings, stone sculptures, historic buildings. The removal of salts from these objects is however difficult and often poultices are used. In these methods a wet poultice is applied to the surface of the substrate to be treated and is kept in place for some period of time before being removed. Many studies up to now on poulticing have focused on the salt and moisture transport solely in terms of advection and diffusion. The objective of this study is to demonstrate the potential contribution of osmotic pressure to salt extraction during poulticing treatments. To this end we have conducted a series of experiments where we have measured the moisture and salt transport during poulticing for some well defined materials. Here we have used nuclear magnetic resonance to measure non-destructively the moisture and ion transport during these experiments. This study shows that osmotic pressure can exert a significant influence on salt extraction by poulticing methods during drying. Importantly, as salt is transported from the substrate and into the poultice, this results in a build-up of osmotic pressure within the poultice decreasing the effective pore-size of the poultice. Therefore the build-up of osmotic pressure enhances the salt extraction and thus increases the efficiency of the poulticing treatment.