The porous structure of second- and third-generation polyphenylene-type dendrimers was investigated by adsorption of N2, Ar, and CO2 gases, scanning electron microscopy and small-angle X-ray spectroscopy. Rigid dendrimers in bulk are microporous and demonstrate a molecular sieve effect. When using CO2 as an adsorbate gas, the pore size varies from 0.6 to 0.9 nm. This is most likely due to the distances between dendrimer macromolecules or branches of neighboring dendrimers, whose packing is mostly realized due to intermolecular interactions, in particular, π–π interactions of aromatic fragments. Intermolecular interactions prevent the manifestation of the porosity potential inherent to the molecular 3D structure of third-generation dendrimers, while for the second generation, much higher porosity is observed. The maximum specific surface area for the second-generation dendrimers was 467 m2/g when measured by CO2 adsorption, indicating that shorter branches of these dendrimers do not provide dense packing. This implies that the possible universal method to create porous materials for all kinds of rigid dendrimers is by a placement of bulky substituents in their outer layer.