Power systems are undergoing a transition from centralised generation to distributed renewable generation. That calls for more flexibility in balancing generation and consumption because distributed energy resources in most cases rely on weather-dependent resources and can, therefore, only be controlled to a certain degree. The necessary flexibility can be achieved by introducing digitalisation. However, digitalisation also leads to new vulnerabilities of the power system and increases its complexity. Additionally, the often rapid and unforeseeable development of information and communication technology introduces a new level of uncertainty in the system design. These circumstances make it necessary to shift from a classical design of robust to the design of resilient power systems that are able to anticipate, react to, and recover from them. In this paper, these real-time attributes of a resilient digitalised power system are analysed with respect to potential measures: an enhanced situational awareness, virtualisation, flexibilisation, and a distributed black start. The measures tackle different challenges for resilient digitalised power systems and cover different phases of the resilience process, visualised in the so-called resilience bathtub curve. The implementation of these measures can increase the resilience of a digitalised power system and are meant to be combined with further, also non-real-time measures.