Judging quality
Look for a repeating radial floret pattern rather than random banding, and for silicified hardness — genuine agatised coral will not scratch with a steel blade.
Fossil
Colonial coral replaced by agate or chalcedony, preserving the flower-like corallite pattern as a permanent stone. Florida agatised coral shows crisp white florets in grey; Petoskey stone from Michigan is a Devonian rugose coral polished to a honeycomb.

Look for a repeating radial floret pattern rather than random banding, and for silicified hardness — genuine agatised coral will not scratch with a steel blade.
Durable. Wash with water; Petoskey stone benefits from occasional light waxing to keep the pattern visible when dry.
Petoskey stone is the state stone of Michigan and is named for the Odawa leader Chief Pet-O-Sega.
Cultural history, recorded as tradition rather than as medical or scientific claim.
See it in person
Both rooms are open six days a week, and there is always someone happy to pull pieces out of the case so you can compare them under the light.