Motivated by climate change, increasing industrialization and energy reliability concerns, the smart grid is set to revolutionize traditional power systems. Moreover, the exponential annual rise in number of grid-connected users and emerging key players e.g. electric vehicles strain the limited radio resources, which stresses the need for novel and scalable resource management techniques. Digital twin is a cutting-edge virtualization technology that has shown great potential by offering solutions for inherent bottlenecks in traditional wireless networks. In this article, we set the stage for various roles digital twinning can fulfill by optimizing congested radio resources in a proactive and resilient smart grid. Digital twins can help smart grid networks through real-time monitoring, advanced precise modeling and efficient radio resource allocation for normal operations and service restoration following unexpected events. However, reliable real-time communications, intricate abstraction abilities, interoperability with other smart grid technologies, robust computing capabilities and resilient security schemes are some open challenges for future work on digital twins.