This article describes the experimental investigation of Cosserat (or micropolar) elasticity and surface damage effects in closed-cell polymethacrylimide foams of different densities. The method of size effects was used to find the degree of Cosserat behaviour for both cylindrical and square cross-section specimens in bending and torsion. The foams were found to behave as Cosserat materials in which slender specimens appear less stiff than thick ones, provided sufficient care is taken when machining the specimens. Surface damage caused by the machining process may cause the apparent stiffness to decrease with decreasing specimen size, giving an opposite softening size effect.