Lightweight materials for efficient electromagnetic interference shielding over a wide range of frequency are of great interest. Aerogels of multi-walled carbon nanotubes (MWCNTs) distributed in a dielectric matrix may interact effectively with electromagnetic radiation. Moreover, being arranged in specific patterns, they can also provide metamaterial characteristics (e.g., negative refractive index). In the present paper, we have studied the interaction between two spheres of the carbon nanotube aerogels in order to obtain a comprehensive basis for producing periodic 2D and 3D structures of such aerogel spheres in a dielectric matrix. We have extended the open resonator technique to the case of two units of MWCNT aerogels in order to reveal the interaction between them. The performance of the system depends on the orientation of the electric field to the axis of the aerogel cluster: MWCNT aerogel spheres (d = 4.5 mm) interact considerably at the gap between spheres ∼0.2λ (11.6 GHz) for perpendicular orientation, while, in case of axial orientation, the interaction is negligible even at the distances close to the contact between aerogels (∼0.02λ). Additionally, the cluster of two carbon nanotube aerogel spheres provides the polarizability close to that of copper spheres while having only 1% of their weight.