Deep, ground-based, optical wide-field supernova searches are capable of detecting a large number of supernovae over a broad redshift range up to z similar to 1.5. While it is practically infeasible to obtain spectroscopic redshifts of all supernova candidates right after their discovery, we show that the magnitudes and colors of the host galaxies, as well as the supernovae, can be used to select high-z supernova candidates for subsequent spectroscopic and photometric follow-up. Using Monte Carlo simulations we construct criteria for selecting galaxies in well-defined redshift bands. For example, with a selection criterion using B-R and R-I colors we are able to pick out potential host galaxies for which z greater than or equal to 0.85 with an 80% confidence level and with a selection efficiency of 64%-86%. The method was successfully tested using real observations from the Hubble Deep Field. Similarly, we show that the magnitude and colors of the supernova discovery data can be used to constrain the redshift. With a set of cuts based on V-R and R-I in a search to m(1) similar to 25, supernovae at z similar to 1 can be selected in a redshift interval sigma(z)less than or equal to0.15.