Computational intelligence methods have been widely applied to model-based engine calibration. Engine calibration based on computational fluid dynamics (CFD) calculations is time-consuming and constrained. In this paper, we model a real-world aero-engine calibration problem with many parameters as an expensive optimisation problem with hidden constraints. Two surrogate-assisted meta-heuristic frameworks using offline and online strategies are proposed in this paper for efficient aero-engine calibration. A surrogate model is trained on engine parameter settings, that lead to valid and invalid CFD calculations, to predict the feasibility of new parameter settings. Parameter settings that are predicted as infeasible by the surrogate model will be eliminated for evaluation during search to reduce the time wasted on infeasible solutions. To validate our approaches, instantiation of the offline and online frameworks are implemented with a neural network model and a self-adaptive particle swarm optimisation and verified on calibrating a real aero-engine model. Both the proposed offline and online frameworks significantly speed up the calibration in terms of realtime performance compared with the approach without using a surrogate model. The surrogate model not only improves the calibration efficiency but also is capable of indicating the importance of parameters to guide the calibration order.