We present a novel method for designing controllers for robots with variable impedance actuators. We take an imitation learning approach, whereby we learn impedance modulation strategies from observations of behaviour (for example, that of humans) and transfer these to a robotic plant with very different actuators and dynamics. In contrast to previous approaches where impedance characteristics are directly imitated, our method uses task performance as the metric of imitation, ensuring that the learnt controllers are directly optimised for the hardware of the imitator. As a key ingredient, we use apprenticeship learning to model the optimisation criteria underlying observed behaviour, in order to frame a correspondent optimal control problem for the imitator. We then apply local optimal feedback control techniques to find an appropriate impedance modulation strategy under the imitator's dynamics. We test our approach on systems of varying complexity, including a novel, antagonistic series elastic actuator and a biologically realistic two-joint, six-muscle model of the human arm.