A generic search is presented for the associated production of a Z boson or a photon with an additional unspecified massive particle X, pp -> pp + Z/gamma + X, in proton-tagged events from proton-proton collisions at root s = 13 TeV, recorded in 2017 with the CMS detector and the CMS-TOTEM precision proton spectrometer. The missing mass spectrum is analysed in the 600-1600 GeV range and a fit is performed to search for possible deviations from the background expectation. No significant excess in data with respect to the background predictions has been observed. Model-independent upper limits on the visible production cross section of pp -> pp + Z/gamma + X are set.