This article proposes two control methods for performing a backflip maneuver with miniature quadcopters. First, an existing feedforward control approach is improved by finding the optimal sequence of motion primitives via Bayesian optimization, using a surrogate Gaussian process (GP) model. To evaluate the cost function, the flip maneuver is performed repeatedly in a simulation environment. The second method is based on closed-loop control and it consists of two main steps: first, a novel robust, adaptive controller is designed to provide reliable reference tracking even in case of model uncertainties. The controller is constructed by augmenting the nominal model of the drone with a GP that is trained using measurement data. Second, an efficient trajectory planning algorithm is proposed, which designs feasible trajectories for the flip maneuver using only quadratic programming. The two approaches are analyzed in simulations and in real experiments using Bitcraze Crazyflie 2.1 quadcopters.