Place the limes cut-side down on the grill along with the skewered strawberries and cook until charred, 3 to 5 minutes. Allow the limes and strawberries to cool, then juice the limes, enough to get 2 ounces.
Rim 2 margarita or rocks glasses with salt, if desired, by dipping the rim in lime juice, water or extra triple sec, then in the salt. Place the agave, mezcal, grilled lime juice, grilled strawberries and triple sec in a blender along with 1 cup ice. Blend for 30 seconds. Pour into rimmed glasses. Garnish with a strawberry or lime.