Naval ships can be constructed using sandwich composite structures with the core material being polymer foam or balsa wood. Naval ships are at risk from explosive blasts from underwater and airborne munitions, and therefore the sandwich structures used must be resistant to extreme deformation and damage caused by blast loads. An experimental study is presented comparing the explosive blast response of sandwich composite panels with a polymer foam (PVC) core or balsa core with polymer laminate facesheets reinforced carbon or glass fibres. These materials studied are representative of sandwich structures used on naval ships. Sandwich panels were subjected to small-scale explosive air blasts of increasing shock wave impulse loads. The out-of-plane deformation and damage was influenced by both the facesheet laminate material and the core material. The fibreglass laminate facesheets were more resistant to blast-induced damage than the carbon fibre facesheets. The blast damage to the facesheet-core interfaces and within the core was more extensive using balsa compared to polymer foam. The study provides new insights into the relative blast performance of different types of sandwich structures used in naval ships.