The paper elucidates the methods of estimating damping in ceramic matrix composites (CMC) with matrix cracks. Unidirectional composites with bridging matrix cracks and cross-ply laminates with tunneling cracks in transverse layers and bridging cracks in longitudinal layers are considered. It is shown that bridging matrix cracks may dramatically increase damping in unidirectional CMC due to a dissipation of energy along damaged sections of the fiber-matrix interface (interfacial friction). Such friction is absent in the case of tunneling cracks in transverse layers of cross-ply laminates where the changes in damping due to a degradation of the stiffness remain small. However, damping in cross-ply laminates abruptly increases if bridging cracks appear in the longitudinal layers.