We report on a measurement of the fraction of events with a W or Z boson which are produced diffractively inpp collisions at √ s = 1.96 TeV, using data from 0.6 fb −1 of integrated luminosity collected with the CDF II detector equipped with a Roman-pot spectrometer that detects thep from p + p →p + [X + W/Z]. We find that (1.00 ± 0.11)% of W s and (0.88 ± 0.22)% of Zs are produced diffractively in a region of antiproton or proton fractional momentum loss ξ of 0.03 < ξ < 0.10 and 4-momentum transferred squared t of −1 < t < 0 (GeV/c) 2 , where we account for the events in which the proton scatters diffractively while the antiproton dissociates,p + p → [X + W/Z] + p, by doubling the measured proton dissociation fraction. We also report on searches for W and Z production in double Pomeron exchange, p +p → p + [X + W/Z] +p, and on exclusive Z production, p + p →p + Z + p. No signal is seen above background for these processes, and comparisons are made with expectations.