Judging quality
Test the color: many blue and green 'calcites' on the market are dyed. Optical clarity, sharp rhombohedral cleavage and a strong fizz in weak acid identify true calcite.
Carbonate
One of the most polymorphic minerals known, with hundreds of crystal habits and every color of the spectrum. Optical calcite from Iceland splits an image in two through double refraction.

Test the color: many blue and green 'calcites' on the market are dyed. Optical clarity, sharp rhombohedral cleavage and a strong fizz in weak acid identify true calcite.
Soft and acid-sensitive. Keep away from vinegar, citrus and household cleaners; dust dry.
Viking navigators may have used Icelandic optical calcite as a 'sunstone' to locate the sun through overcast skies.
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.