  We develop a new method for estimating the redshift of galaxy clusters
through resolved images of the Sunyaev-Zel'dovich effect (SZE). Our method is
based on morphological observables which can be measured by actual and future
SZE experiments. The method is tested using a set of high resolution
hydrodynamical simulations of galaxy clusters at different redshifts. The
method combines the observables in a principal component analysis. We show how
this can give an estimate of the redshift of the galaxy clusters. Although the
uncertainty in the redshift estimation is large, the method should be useful
for future SZE surveys where hundreds of clusters are expected to be detected.
A first preselection of the high redshift candidates could be done using our
proposed morphological redshift estimator.
