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A less obvious, but important, step is to explore different error conditions in your federating software and/or application; consider what problems are likely to recur in production and how users ought to be advised to proceed. For example, consider how bookmarks of various kinds, or the use of the back button, influences the user experience. Turn those otherwise useless messages into a straightforward warning about these features.
The hand-off between SPs and IdPs within a federation can result in user confusion when errors occur. See Federated Error Handling for ways to address this.
Finally, translate overly technical messages into customized responses in plain language that lead users to solutions; most software will provide the capability to do this. Even if error message testing breaks after upgrades, a deployment is no worse off for having improved the experience in the meantime.