Can invisible objects be `seen' via forward proton detectors at the LHC?

We discuss the possibility of identifying invisible objects (e.g. dark matter) via missing mass in Central Exclusive Processes; that is, in events where only forward protons are detected at the LHC. We show that the signal must have a cross section greater than 0.25 fb in order that it can be detected. We estimate the huge background caused by soft proton dissociation and evaluate the requirements of the detector `veto' system needed to sufficiently suppress these events. In addition, we discuss the related process leading to the possible identification of the particles from the so-called `compressed-mass Beyond the Standard Model (BSM)' scenarios. In this case the background is not so severe.