  Photometric redshift (photo-z) estimates are playing an increasingly
important role in extragalactic astronomy and cosmology. Crucial to many
photo-z applications is the accurate quantification of photometric redshift
errors and their distributions, including identification of likely catastrophic
failures in photo-z estimates. We consider several methods of estimating
photo-z errors and propose new training-set based error estimators based on
spectroscopic training set data. Using data from the Sloan Digital Sky Survey
and simulations of the Dark Energy Survey as examples, we show that this method
provides a robust, relatively unbiased estimate of photo-z errors. We show that
culling objects with large, accurately estimated photo-z errors from a sample
can reduce the incidence of catastrophic photo-z failures.
