Sustainable software systems aim to create resource-efficient software products and reduce the carbon impact of applications. Current approaches for sustainability assessment of software are either only focused on their operation or rely on methods in their engineering. More holistic approaches for sustainable software system spanning are missing. Thus, we are interested in the engineering of sustainable software systems together with the monitoring of their sustainability goals over their whole lifetime. Within this paper, we suggest using digital twins to accompany software systems in all life cycle phases with a specific focus on using model-driven engineering methods for the creation of applications. We can generate accompanying digital twins which share relevant models and data with the actual system and provide services for the assessment of sustainability indicators. In the long run, this provides us with better assessment options for software systems.