Data-driven surrogate modelling of antenna structures is an attractive way of accelerating the design process, in particular, parametric optimization. In practice, construction of surrogates is hindered by curse of dimensionality as well as wide ranges of geometry parameters that need to be covered in order to make the model useful. These difficulties can be alleviated by constrained performance-driven modelling with the surrogate domain spanned by a set of reference designs optimized with respect to selected figures of interest. Unfortunately, uniform training data allocation in such constrained domains is a nontrivial task. This paper proposes a new design of experiments technique which ensures sampling uniformity. Our approach is based on uniform sampling on the domain-spanning manifold and linear transformation of the remaining sample vector components onto orthogonal directions (w.r.t. the manifold). The proposed procedure is demonstrated using two antenna examples and shown to ensure considerable improvement of the surrogate model accuracy as compared to rudimentary random sampling. Application examples are also provided.