We report on a measurement of the fraction of events with a W or Z boson which are produced diffractively in p̄p collisions at √s=1.96TeV, using data from 0.6fb⊃-1 of integrated luminosity collected with the CDFII detector equipped with a Roman-pot spectrometer that detects the p̄ from p̄+p→p̄+[X+W/Z]. We find that (1.00±0.11)% of Ws 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, p̄+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+p̄→p+[X+W/Z]+p̄, and on exclusive Z production, p̄+p→p̄+Z+p. No signal is seen above background for these processes, and comparisons are made with expectations. © 2010 The American Physical Society.