This paper presents a Compactly-Supported, Radial Basis Functions (CSRBFs) method for building the polymer, extra-stress tensor arising in micro-macro simulations of particle-based, viscoelastic, free-surface flows. The extra-stress tensor is reconstructed on the domain and evaluated at the mesh-nodes by CSRBFs using the known values of the tensor at each of the ensembles of dumbbells which carry the molecular information of the non-Newtonian fluid, circumventing the need for ad-hoc methodologies entailing repositioning/creation/destruction of polymer particles. The macroscopic equations and free-surface representation are then discretized using available finite element techniques. The versatility, computational performance and potential of the CSRBF technique is illustrated with simulations of 2d Newtonian bubbles rising in a viscoelastic fluid using the Hooke and FENE kinetic models with highly refined meshes under strong density and viscosity ratios. The results show the ability of the method to accurately build the polymer stress tensor in flows featuring intense viscoelastic effects, while opening the way for adaptive, isotropic or anisotropic, mesh refinement procedures. (c) 2015 Elsevier B.V. All rights reserved.