Place the mustard, vinegar and oil in a small bowl and whisk to combine. Stir in the tarragon and season with salt and pepper.
Place the lobster tails on a medium-hot barbecue, flesh-side down and cook for 6 minutes. Turn the tails over and spoon 1 tablespoon of dressing over the flesh of each lobster, then cook for a further 10–15 minutes, or until cooked through. This is best done with the lid of the barbecue down if you have one.
Serve the lobster tails with the remaining dressing.