But even in exception-based languages there is still a lot of code that tests returned values to determine whether to carry on or go down some error-handling path
The key to taming exceptions is to use them differently. Any exception that escapes a method means that the method has failed to meet its specification, and therefore you will need to clean up and abort at some level in the call chain. But you don't need to catch at every level (unless your language forces you to), nor should you need to do anything that relies on the "meaning" of the exception. Instead, you take a local action: close a file, roll back the database, prompt the user to save or abandon, etc, and either re-throw or not according to whether you have restored normality. There will only be a few places in your app where this type of cleanup is needed.
If you're not doing it this way, you're using exceptions as a control structure, and that's never going to be clean.