Preheat a grill for medium heat and lightly oil the grate.
Whisk olive oil, basil, thyme, salt, and pepper together in a bowl. Allow flavors to meld for 5 minutes. Brush oil mixture over the cut side of each peach half.
Grill peaches, cut-sides down, on the preheated grill until softened and grill marks appear, about 4 minutes.