Impact damage can significantly reduce the strength of composite sandwich panels, giving rise to large factors of safety in design. A self-healing sandwich panel was designed and manufactured. Specimens were tested in edgewise compression-after-impact to prove the concept. The self-healing system consists of vascular networks carrying the two liquid components of an epoxy resin system. After damage and autonomous self-healing, the specimens could be restored to their undamaged strength. Key influences on healing efficiency, and the need for further improvements in reliability were identified. A simple specific strength analysis suggested that the mass penalty of self-healing could, in some cases, be offset by the improved design allowables permitted.