  We report on a measurement of the fraction of events with a W or Z boson
which are produced diffractively in antiproton-proton collisions at a center of
mass energy of 1.96 TeV, using data from 0.6 inverse femtobarns of integrated
luminosity collected with the CDF-II detector equipped with a Roman-pot
spectrometer that detects the antiproton (pbar) from pbar+p --> pbar+[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
(\xi) of 0.03<\xi<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, pbar+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+pbar --> p+[X+W/Z]+pbar,
and on exclusive Z production, pbar+p --> pbar+Z+p. No signal is seen above
background for these processes, and comparisons are made with expectations.
