Short answer
Gruta do Carvão is on São Miguel (Ponta Delgada) and Algar do Carvão is on Terceira; both are volcanic caves visited only with guided tours. Tours have specific schedules and limited capacity, so book ahead through official channels and confirm opening times locally. Bring a jacket, as caves are cool and sometimes damp.
General information, not legal or tax advice. Rules and amounts change: confirm with official sources.