We investigated the cavity structure by the deformation of a unit cell of a Composite Metamaterial (CMM) structure. We considered different cavity structures with different resonance frequencies and Q-factors. We observed the Q-factor of the cavity resonance as 108 for a CMM based single cavity wherein the cavity structure is a closed ring structure. We investigated the reduced photon lifetime and observed that at the cavity resonance, the effective group velocity was reduced by a factor of 20 for a CMM based single cavity compared to the electromagnetic waves propagating in free space. Since the unit cells of metamaterials are much smaller than the operation wavelength, subwavelength localization is possible within these metamaterial cavity structures. We found that the electromagnetic field is localized into a region of/8, where is the cavity resonance wavelength. Subsequently, we brought two cavities together with an intercavity distance of two metamaterial unit cells and then investigated the transmission spectrum of CMM based interacting 2-cavity system. Finally, using the tight-binding picture we observed the normalized group velocity corresponding to the coupled cavity structure.