Conventional window technologies tend to have poor thermal transmittance coefficients (U-values) which cause significant heat loss during the winter season and undesired heat gain in the summer. This study reports a new procedure to calculate center glass U-values of triple and quadruple windows which include low-emissive radiant energy veils - shades and blinds with spectrally selective coatings - between the outermost glass panes. A numerical zonal model is developed to simulate a net radiation system coupled with finite difference and ray tracing methods using validated derived experimental equations. A parametric investigation is carried out wherein the influence of different parameters such as optical properties, inter-pane distances and slat angles of the blinds on the thermal performance of the glazing system are analyzed. Three different gas fill types are examined under realistic boundary conditions. It is shown that this window system has a compelling U-value compared to ordinary multilayer glazing products. (C) 2019 Elsevier Ltd. All rights reserved.