We report on a measurement of the fraction of events with a W or Z boson which are produced diffractively in pp 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 the p from p+p→p+[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<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.