Data-driven models, or metamodels, offer an efficient way to mimic the behaviour of computation-intensive simulators. Subsequently, the usage of such computationally cheap metamodels is indispensable in the design of contemporary antenna structures where computationintensive simulations are often performed in a large scale. Although metamodels offer sufficient flexibility and speed, they often suffer from an exponential growth of required training samples as the dimensionality of the problem increases. In order to alleviate this issue, a Gaussian process based approach, known as Gradient Enhanced Kriging, is proposed in this work to achieve cost-efficient modeling of antenna structures. The Gradient Enhanced Kriging approach incorporates adjoint-based sensitivity data in addition to function data obtained from electromagnetic simulations. The approach is illustrated using a dielectric resonator and an ultra-wideband antenna structures. The method demonstrates significant accuracy improvement with less number of training samples over the Ordinary Kriging approach which utilises function data only. The discussed technique has been favorably compared with Ordinary Kriging in terms of computational cost.