Thermal insulation of building envelope plays a key-role in energy saving: a growing interest is focused on new materials, such as the recycled and sustainable ones. Innovative mineral fiber insulating panels were developed and investigated as a strategy for building refurbishment. The thermal and acoustic properties were investigated in order to compare them to conventional solutions. The thermal conductivity was evaluated by means of a Heat Flow meter apparatus: it is in the 0.031−0.034 W/(m K) range, depending on the density. The acoustic absorption coefficient and the Transmission Loss values measured by means of Kundt’s Tube showed a very good acoustic behavior, when compared to conventional solutions with similar chemical composition, but worse mechanical resistance, such as rock wool panels. The low value of thermal conductivity (0.0312 W/(m K) for a density of 165 kg/m3), together with other characteristics such as acoustic insulation improvement, sustainability (very low presence of additives, such as resin), mechanical resistance, high resistance to fire, and finally easy application in buildings with very low thicknesses (9−27 mm) suggest this solution as a very useful one for building refurbishment, especially for historical buildings.