Scrub the oysters and rinse the clams. Heat the grill to medium-high.
Lay the clams in a single layer on the grate, place the oysters on the more thickly curved halves of their shells to retain their juices, and close the grill. The clams and oysters will open after six or seven minutes.
Remove them from the heat, add a spritz of lemon or a dash of hot sauce and place them on a platter lined with kosher salt. Voila! Summer's easiest and quickest hors d'oeuvre.