Poly(hydromethylsiloxane) (PHMS) was cross-linked with 1,3,5,7-tetramethyl-1,3,5,7-tetravinylcyclotetrasiloxane (D4Vi) in water-in-oil High Internal Phase Emulsions to form macroporous materials known as polyHIPEs. It was shown that in the process of pyrolysis under Ar atmosphere at 520 °C, the obtained polyHIPEs were converted to ceramers with high yields (82.8–88.0 wt.%). Structurally, the obtained ceramers were hybrid ceramics, i.e., they consisted of Si-O framework and preserved organic moieties. Macropores present in the polyHIPE precursors remained in ceramers. Ceramers contained also micro- and mesopores which resulted from the precursor’s mass loss during pyrolysis. Total pore volume and BET specific surface area related to the existence of micro- and mesopores in ceramers depended on the PHMS: D4Vi ratio applied in polyHIPE synthesis. The highest total pore volume (0.143 cm3/g) and specific surface area (344 m2/g) were reached after pyrolysis of the precursor prepared with the lowest amount of D4Vi as compared to PHMS. The composite materials obtained after deposition of PdO nanoparticles onto ceramers followed by reduction of PdO by H2 were active and selective catalysts for phenylacetylene hydrogenation to styrene.