Preheat the oven to 350 degrees.
In a medium saucepan, combine the cherries, honey, vinegar, 2 tablespoons of the basil and a pinch of salt. Cook over medium low heat for 5 minutes, stirring occasionally, until the cherries are just starting to release their juice. Remove from the heat and let cool slightly.
Meanwhile, arrange bread slices on a sheet pan. Brush lightly with olive oil, sprinkle with salt and pepper, and bake for 10 minutes, or until lightly toasted.
To assemble the crostini, spread a layer of goat cheese onto each slice, then top with a spoonful of cherries. Sprinkle the remaining 2 tablespoons of basil over the crostini and serve immediately.
Note: While you can make the cherry mixture in advance, the longer it sits, the more the cherries lose their bright red color. I would recommend making them right before serving.