We combine second order local regression meta-models with the Covariance Matrix Adaptation Evolution Strategy in order to enhance its efficiency in the optimization of computationally expensive problems. Computationally intensive direct numerical simulations of an anguilliform swimmer provide the testbed for the optimization. We propose two concepts to reduce the computational cost of the meta-model building. The novel versions of the local meta-model assisted Evolution Strategy are tested on benchmark problems and compared to results from literature. The results demonstrate that the use of local meta-models increases significantly the efficiency of already competitive evolution strategies and that the model building cost can be successfully reduced. The meta-model assisted Evolution Strategy is applied to the optimization of the swimming motion of a three-dimensional, self-propelled eel-like body. The motion of the self-propelled body is determined by a set of parameters but the motion is not prescribed apriori. Instead here we introduce the concept of identifying the swimming motion parameters from an evolutionary optimization procedure. The optimization successfully identifies a motion pattern that is 30% more efficient than an existing reference motion pattern. During the efficient swimming motion, the deformation of the body is extended along its length in a controlled fashion.