A proposed wall system that will provide a high thermal resistance in a relatively thin profile incorporates vacuum insulation panels (VIP) enclosed within closed-cell insulating foam. In addition to providing some additional thermal resistance, the foam protects the vacuum panels during construction and provides a surface appropriate for an adhesive joint on both sides of the foam-VIP unit. Multiple configurations of the composite structure were considered and experimental measurements were sought to provide more information in the final selection. Small subsections of each candidate arrangement were prepared and tested in a special-purpose heat flux meter apparatus. Those measurements are described here, along with additional modeling efforts based on these smaller-scale measurements. The focus of the tests reported here is to investigate the impact of vacuum panel size, the type of foam used to encase the vacuum panels, the thickness and shape of the foam sections between panels, and possible adhesive effects. A new procedure was developed to map the heat flux meter measurement results onto full-scale wall designs to predict the system thermal performance. Several potential arrangements of the foam-VIP unit were also evaluated using a finite-difference methodology. The report also evaluates procedures for testing VIPs in a heat flux meter apparatus, and makes some recommendations.