We evaluate, in a model-independent way, the signal-to-background ratio for Higgs -> b bbar detection in exclusive double-diffractive events at the Tevatron and the LHC. For the missing-mass approach to be able to identify the Higgs boson, it will be necessary to use a central jet detector and to tag b quark jets. The signal is predicted to be very small at the Tevatron, but observable at the LHC. However we note that the background, that is double-diffractive dijet production, may serve as a unique gluon factory. We also give estimates for the double-diffractive production of chi_c and chi_b mesons at the Tevatron. We emphasize that a high-resolution missing-mass measurement, on its own, is insufficient to identify rare processes.