  A search for the central exclusive production of top quark-antiquark pairs
($\mathrm{t\bar{t}}$) is performed for the first time using proton-tagged
events in proton-proton collisions at the LHC at a centre-of-mass energy of 13
TeV. The data correspond to an integrated luminosity of 29.4 fb$^{-1}$. The
$\mathrm{t\bar{t}}$ decay products are reconstructed using the central CMS
detector, while forward protons are measured in the CMS-TOTEM precision proton
spectrometer. An observed (expected) upper bound on the production cross
section of 0.59 (1.14) pb is set at 95% confidence level, for collisions of
protons with fractional momentum losses between 2 and 20%.
