The aerodynamics of hovering flight in a hawkmoth (Manduca sexta) are examined using a computational modelling approach which combines a low-fidelity blade-element model with a high-fidelity Navier–Stokes-based flow solver. The focus of the study is on understanding the optimality of the hawkmoth-inpired wingstrokes with respect to lift generation and power consumption. The approach employs a tight coupling between the computational models and experiments; the Navier–Stokes model is validated against experiments, and the blade-element model is calibrated with the data from the Navier–Stokes modelling. In the first part of the study, blade-element and Navier–Stokes modelling are used concurrently to assess the predictive capabilities of the blade-element model. Comparisons between the two modelling approaches also shed insights into specific flow features and mechanisms that are lacking in the lower-fidelity model. Subsequently, we use blade-element modelling to explore a large kinematic parameter space of the flapping wing, and Navier–Stokes modelling is used to assess the performance of the wing-stroke identified as optimal by the blade-element parameter survey. This multi-fidelity optimization study indicates that even within a parameter space constrained by the animal’s natural flapping amplitude and frequency, it is relatively easy to synthesize a wing stroke that exceeds the aerodynamic performance of the hawkmoth wing stroke. Within the prescribed constraints, the optimal wing stroke closely approximates the condition of normal hover, and the implications of these findings on hawkmoth flight capabilities as well as on the issue of biomimetic versus bioinspired design of flapping wing micro-aerial vehicles, are discussed.