In this study, we prepared a series of conjugated microporous polymers (CMPs) through Sonogashira-Hagihara cross-couplings of a tetrabenzonaphthalene (TBN) monomer with pyrene (Py), tetraphenylethylene (TPE), and carbazole (Car) units and examined their chemical structures, thermal stabilities, morphologies, crystallinities, and porosities. TBN-TPE-CMP possessed a high surface area (1150 m² g^-1) and thermal stability T_d10 = 505 °C; char yield = 68 wt %) superior to those of TBN-Py-CMP and TBN-Car-CMP. To improve the conductivity of the TBN-CMP materials, we blended them with highly conductive single-walled carbon nanotubes (SWCNTs). Electrochemical measurements revealed that the TBN-Py-CMP/SWCNT nanocomposite had high capacitance (430 F g^-1) at a current density of 0.5 A g^-1 and outstanding capacitance retention (99.18%) over 2000 cycles; these characteristics were superior to those of the TBN-TPE-CMP/SWCNT and TBN-Car-CMP/SWCNT nanocomposites.