When discussing how to improve side-channel resilience of a cipher, an obvious direction is to use various masking or hiding countermeasures. However, such schemes come with a cost, e.g. an increase in the area and/or reduction of the speed. When considering lightweight cryptography and various constrained environments, the situation becomes even more difficult due to numerous implementation restrictions. However, some options are possible like using S-boxes that are easier to mask or (more on a fundamental level), using S-boxes that possess higher inherent side-channel resilience. In this paper we investigate what properties should an S-box possess in order to be more resilient against side-channel attacks. Moreover, we find certain connections between those properties and cryptographic properties like nonlinearity and differential uniformity. Finally, to strengthen our theoretical findings, we give an extensive experimental validation of our results.