  We present first predictions of the cross sections and differential
distributions for the exclusive reaction $pp \to pp K^{*0} \bar{K}^{*0}$
contributing to the $K^{+} K^{-} \pi^{+} \pi^{-}$ channel. The amplitudes for
the reaction are formulated within the nonperturbative tensor-pomeron approach.
We consider separately the $f_{2}(1950)$ $s$-channel exchange mechanism and the
$K^{*0}$ $t/u$-channel exchange mechanism, focusing on their specificities.
First mechanism is a candidate for the central diffractive production of tensor
glueball and the second one is an irreducible continuum. We adjust parameters
of our model, assuming the dominance of pomeron-pomeron fusion, to the WA102
experimental data. We find that including the continuum contribution alone one
can describe the WA102 data reasonably well. We present predictions for the
reaction $pp \to pp (K^{*0} \bar{K}^{*0} \to K^{+} K^{-} \pi^{+} \pi^{-})$ for
the ALICE, ATLAS, CMS and LHCb experiments including typical kinematical cuts.
We find from our model a cross sections of $\sigma \cong 17-250$ nb for the LHC
experiments, depending on the assumed cuts. Absorption effects are included in
our analysis.
