A circular reference was detected while serializing an object

Recently I came across this exception while working on a making a script PowerShell v2 compatible:

Exception calling "Serialize" with "1" argument(s): "A circular reference was detected while serializing an object of type 'System.Management.Automation.PSParameterizedProperty'."

It turns out that this isn’t a “data” issue as most of the stackoverflow answers seem indicate. Well, it probably is under the hood, but all that was required to fix...