Abstract: Quantum mechanical methods are employed to obtain superelastic cross sections involving H(2) and N(2) molecules, in excited rotational states, colliding with electrons at the very low collision energies which are encountered in cold trap experiments. This computational analysis intends to explore the feasibility of cold electrons for the collisional quenching of molecular gases down to the nanokelvin regimes. The results are obtained using rigorous coupled-channel (CC) calculations in the laboratory frame of reference which allows one to correctly describe the cross section behaviour at ultralow energies. The results are analysed down to the ultracold region of validity of Wigner's law, where it is found that electron-driven collisions exhibit substantial efficiency for the quenching of rotational populations in molecular gases involving the title systems.