For the purpose of gaining larger streaming potential, it has been suggested to employ superhydrophobic microchannels with a large velocity slip. There are two kinds of superhydrophobic surfaces, one having a smooth wall with a large Navier slip coefficient caused by the hydrophobicity of the wall material, and the other having a periodic array of no-shear slots of air pockets embedded in a nonslip wall. The electrokinetic flows over these two superhydrophobic surfaces are modelled using the Navier-Stokes equation and convection-diffusion equations of the ionic species. The Navier slip coefficient of the first kind surfaces and the no-shear slot ratio of the second kind surfaces are similar in the sense that the volumetric flow rate increases as these parameter values increase. However, although the streaming potential increases monotonically with respect to the Navier slip coefficient, it reaches a maximum and afterward decreases as the no-shear ratio increases. The results of the present investigation imply that the characterization of superhydrophobic surfaces employing only the measurement of volumetric flow rate against pressure drop is not appropriate and the fine structure of the superhydrophobic surfaces must be verified before predicting the streaming potential and electrokinetic flows accurately.