The goal is to sear the flat side of the split fruits at just the right temperature, so their sugars caramelize but don't burn.
Then you flip the flat side over, apply a glaze to it and leave the fruit halves on the heat long enough to set the glaze, without burning the skin side (bottom) of the fruit.
I'm hardly an expert, since I have done it a total of once. On the other hand, I grilled a few hundred split peaches and plums in my single experience, so I know more than many cooks.
You have a few choices here. If you are using a charcoal or gas grill, you can sear the fruits right on the grill, or put a cast iron skillet on the grill and sear the fruits in the skillet. I would recommend the latter.
Alternately, you can sear the fruits right on your stove, using the pan of your choice. I'm sure it would work fine, and allow you to control the heat better. On the other hand, the smoky flavor of the fire goes well with peaches, and there is something mystical and primordial about the open flame.
Grilled stonefruits
Ingredients (serves 20 or so)
About 20 peaches or plums, halved, pits removed
1/2 cup of peach jam, preferably homemade
1/2 teaspoon salt
1/2 teaspoon cinnamon
Spanish sherry vinegar, water and sugar to taste
Olive oil
Preparation
Before splitting fruits, make your glaze. Liquify your jam in a blender, and add water, a few tablespoons at a time, until it blended, but still coats a spoon. Add cinnamon and then sugar, salt and vinegar until you get a taste you prefer - slightly tangy, but still peachy and not too thin.
Split your fruits with a paring knife, remove pits and lay on a sheet pan. Heat a grill or skillet to medium heat. Brush halves with oil. Place on grill. Leave there 3 to 5 minutes, checking frequently with tongs or a spatula.
You will surely have hot spots on your grill or skillet. Adjust heat and move fruits around so they sear evenly. When caramelized but not burnt, flip over, apply glaze with a brush and push to the sides of the heat so the glaze sets, but the bottoms don't burn.
When ready (in a minute or two) place on serving platters and enjoy.

