Natural deep eutectic solvents (NADESs) are considered as green solvents, and due to their promising sustainability, they have been applied in many research fields. In this study, the main goal is to use various NADES systems to replace the traditional solvents used in conservation and restoration to remove varnish layers in a painting. The toxicity of traditional solvents, such as toluene or acetone, is well known in the chemistry field. To replace them, it is important to understand the intrinsic physicochemical properties of a solvent that may act as a substitute. Polarity and solubility are proposed as the best parameters required for this study. The Nile red probe was used to confirm the similarity between the polarity of deep eutectic systems (DESs) and traditional solvents. According to their polarities and Hansen solubility parameters, it is possible to predict the best solvents to solubilize the natural resin varnishes. Besides this, some arithmetic models can also be applied to estimate the critical or thermodynamic properties, which are useful tools to predict the behavior of these solvents. We have further proven the possibility of dissolving natural varnishes such as dammar or mastic in hydrophobic DESs, such as menthol + lauric acid, menthol + decanoic acid, or menthol + thymol.