  We present results on the Central Exclusive Production of charged particle
pairs $h^{+}h^{-}$ ($h = \pi, K, p$), $pp\to p^\prime+h^{+}h^{-}+p^\prime$,
obtained with the STAR experiment at RHIC in proton-proton collisions at a
center-of-mass energy of $\sqrt{s} = 200$ GeV. All final-state particles were
reconstructed, including forward-scattered protons detected in the Roman Pot
system. As a result, the Double Pomeron Exchange (DPE) events were selected and
the non-exclusive backgrounds were efficiently rejected. Differential fiducial
cross sections were measured as functions of observables related to the central
hadronic final state and to the forward-scattered protons. The measured cross
sections were compared to phenomenological model predictions based on the DPE.
We also present preliminary results on the measurement of the same physics
process at higher collision energy $\sqrt{s} = 510$ GeV. The data demonstrate
features similar to those observed at $\sqrt{s} = 200$ GeV.
