mantel

Keeping mantel and mantle straight is relatively simple.

Mantel in modern English largely does one job: it refers to the shelf above a fireplace. You can remember it by thinking of the "el" in both mantel and shelf.

Mantle on the other hand, does many jobs, including a number that are technical or scientific. Its most common uses are to refer to a literal cloak, mostly of the kind worn in days of yore ("she drew her mantle tighter"), and to a figurative cloak symbolizing authority or importance ("taking on the mantle of the museum's directorship"). It also refers to a general covering in literary uses like "wet earth covered in a mantle of leaves" or "a past shrouded in a mantle of secrecy." And it's also the term for the middle layer of the Earth between the crust and the inner core.

There is, however, a catch to these distinctions: mantle is sometimes used (especially in American English) to refer to the shelf above a fireplace as well—that is, as a synonym of mantel.

This isn't terribly surprising, given the histories of the words. They both derive from the Latin word mantellum, which refers both to a cloak and to a beam or stone supporting the masonry above a fireplace. The words came into use in English a couple centuries apart, but were for a time in the past nothing more than spelling variants.

While it's certainly simpler to use mantle in all cases, mantel is significantly more common as the choice for the shelf, which means it's the safer choice in those cases.