  We present a search for exclusive Z boson production in proton-antiproton
collisions at sqrt(s) = 1.96 TeV, using the CDF II detector at Fermilab. We
observe no exclusive Z->ll candidates and place the first upper limit on the
exclusive Z cross section in hadron collisions, sigma(exclu) < 0.96 pb at 95%
confidence level. In addition, we observe eight candidate exclusive dilepton
events from the quantum electrodynamic process ppbar->gammagamma->p+ll+pbar,
and measure the cross section for M(ll) > 40 GeV/c2 and |eta(l)| < 4 to be
sigma = 0.24^{+0.13}_{-0.10} pb, which is the first measurement for this mass
range and is consistent with the standard model prediction.
