Prepare the margarita glasses. Add coarse sugar to a shallow bowl. Wet the glass rims with a lime wedge and press the glass top in the sugar to coat the rim.
Place the chopped strawberries, orange juice, lime juice and agave into a blender and pulse several times to blend. Taste and if necessary, add more agave. Add crushed ice and pulse until desired consistency is reached. Pour the drink into the prepared glasses.
Garnish each drink with a fresh strawberry with the green leaves on top, slice them half through lengthwise from the bottom and place one on the rim of each glass right before serving.