It is shown that the noise-limited charge sensitivity of a single-electron transistor using superconductors (of either SISIS- or NISIN-type) operating near the threshold of quasiparticle tunneling, can be considerably higher than that of a similar transistor made of normal metals or semiconductors. The reason is that the superconducting energy gap, in contrast to the Coulomb blockade, is not smeared by the finite temperature. We also discuss the increase of the maximum operation temperature due to superconductivity and the peaklike features on the I–V curve of SISIS structures.