Look for bananas that are slightly green on the ends...they will stand the heat much better.
In a saucepan, melt 1/2 stick butter and add 1/2 cup granulated sugar, 2 tablespoons fresh lime juice and 1 teaspoon cinnamon. You can do this on the grill if the pan has a heatproof handle.
Peel 4 bananas and brush with about 1/4 of the butter mixture. Keep the rest for later.
Grill these bananas over medium heat for about 2-4 minutes and turn them once. You are looking for some grill marks on them. After grilling, slice them and add these to the remaining butter sauce. Then you need to put that back on the grill (the whole pan with the bananas and the butter sauce) and cook until heated through....about 5 minutes.