The purpose of this study is threefold: first, to identify a scheme for the determination of the surface energy coefficient a_surf that offers the best compromise between robustness, precision, and numerical efficiency; second, to analyze the correlation between values for a_surf and the characteristic energies of the fission barrier of Pu240; and third, to lay out a procedure how the deformation properties of the Skyrme energy density functional (EDF) can be constrained during the parameter fit. There are several frequently used possibilities to define and calculate the surface energy coefficient a_surf of effective interactions. The most direct access is provided by the model system of semi-infinite nuclear matter, but a_surf can also be extracted from the systematics of binding energies of finite nuclei. Calculations can be carried out either self-consistently (HF), which incorporates quantal shell effects, or in one of the semi-classical Extended Thomas-Fermi (ETF) or Modified Thomas-Fermi (MTF) approximations. The surface energy coefficient of 76 parameterizations of the Skyrme EDF have been calculated. Values obtained with the HF, ETF and MTF methods are not identical, but differ by fairly constant systematic offsets. Despite having some drawbacks compared to the other methods studied here, the MTF approach provides sufficiently precise values for a_surf such that it can be used as a very robust constraint on surface properties during a parameter fit at negligible additional cost. Through the construction of a series of eight parameterizations SLy5s1-SLy5s8 of the standard Skyrme EDF with systematically varied a_surf value it is shown how to arrive at a fit with realistic deformation properties. [Note: The abstract has been abbreviated because of length restrictions imposed by the arXiv. See the paper for the full abstract.]< Réduire