Developments in digital twins are driven by the availability of sensor technologies, big data, first principles knowledge, and advanced analytics. In this paper, we discuss these changes at a conceptual level, presenting a shift from nominal engineering, aiming at design optimisation, to performance engineering, aiming at adaptable monitoring diagnostic, prognostic, and prescriptive capabilities. A key element introduced here is the role of emulators in this transformation. Emulators, also called surrogate models or metamodels, provide monitoring and diagnostic capabilities. In particular, we focus on an optimisation goal combining optimised and robust performance derived from stochastic emulators. We demonstrate the methodology using two open-source examples and show how emulators can be used to complement finite element and computational fluid dynamic models in digital twin frameworks. The case studies consist of a mechanical system and a biological production process.