There is nothing I hate more than getting a cheeseburger with cheese that hasn't been melted all the way. Now, I'm not talking about feta or something that doesn't really melt all that well in the first place. But it's a crying shame when the mozzarella on top of your burger isn't oozing down the sides and making a delicious mess when you bite into it.
Getting the perfect melt is so easy to accomplish. Here's my secret: I use a basting cover, an inexpensive aluminum dome that short-order cooks use in diners. It looks like the lid of a sauté pan, except that it is domed to fit over the burger. A basting cover allows just enough clearance, meaning the cheese doesn't touch and stick to it but the cover can still hold in the heat to melt the cheese beautifully. If you don't have a basting cover, a sturdy metal bowl will also do the trick. Alternatively, you can close the grill cover or you can even tent each burger with a square of aluminum foil.