At the beginning of Poe's classic short story "The Cask of Amontillado," Montresor elaborates on his definition of the perfect revenge. After vaguely describing the ways Fortunato had caused him harm, Montresor provides his definition for the perfect way to get revenge by saying,
I must not only punish, but punish with impunity. A wrong is unredressed when retribution overtakes its redresser. It is equally unredressed when the avenger fails to make himself felt as such to him who has done the wrong. (Poe, 1)
Montresor is essentially saying that he must not only punish his enemy but do so without getting caught. His revenge would not be complete if he were to suffer the consequences of his actions or not make himself known to his enemy. Given Montresor's strict definition of revenge, one could argue that he successfully committed the perfect crime.
Montresor carefully plans and executes the perfect crime by cleverly acting amicably in front of Fortunato and gaining his trust. Montresor is careful to approach Fortunato during the chaotic carnival season, which gives him the opportunity to conceal his identity behind a mask. Montresor then manipulates Fortunato's pride and uses his love of fine wines to persuade his enemy into entering his catacombs.
Once Fortunato is in Montresor's vaults, he continues to give his enemy alcohol to further impair Fortunato's judgment before suddenly shackling him to the back wall. Montresor then builds a wall around Fortunato, burying him alive. At the end of the story, Montresor mentions that for a "half of a century" nobody has disturbed Fortunato's bones, which reveals that he got away with murder.
Since Montresor made himself known to his enemy and never suffered the consequences of murdering Fortunato, one could argue that he committed the perfect crime.