Preparing CAD models for CAE simulations is a major bottleneck when dealing with small geometric features. The process often involves de–featuring, which cannot be fully automated and requires many hours of human interaction because it depends upon the physics considered. The NURBS–enhanced finite element method (NEFEM) decouples the concepts of geometry and solution approximation to avoid this problem. NEFEM describes the geometry using the boundary representation (B–rep) from CAD models, and approximates the solution using polynomial functions. As a result, NEFEM completely removes the error due to geometric approximation and the need for de–featuring. In this paper the meshing strategy in two dimensions is recalled. The proposed approach involves a modified advancing front technique where boundary elements have edges that are described by a collection of boundary curves. The strategy required to utilise the meshes into an existing solver is described and an example is used to demonstrate the benefits of the proposed approach. Next, a novel three dimensional surface mesh generation strategy is presented. The technique starts with an initial FEM mesh, where elements smaller than the user defined spacing are present due to CAD model containing small features. A locally enhanced advancing front method is then used to modify the mesh and ensure that the final mesh contains element sizes that better match the user defined spacing. The resulting surface mesh contains elements that cross intersection curves of the CAD and exactly retain the original B–rep. Several examples are presented to show the potential of the proposed technique.