Combine 4 cups water and 1 teaspoon salt in a medium saucepan and bring to a simmer over medium heat. Gradually add the grits, whisking constantly. Reduce the heat to medium low and cook, stirring occasionally with a wooden spoon, until tender, about 20 minutes. If the grits seem too thick, thin with water, 1 to 2 tablespoons at a time.
Stir in the butter and season with pepper. Remove from the heat and cover to keep warm.