In a bowl, whisk together lime juice and next 6 ingredients. Whisk in oil in a thin stream until emulsified. Pour half of the mixture over tuna and refrigerate for 30- 60 minutes, reserving the other half to baste fish while grilling. Place on a white-hot, well-oiled grill until lightly charred on both sides, but not past medium-rare. Brush with any remaining glaze just before serving.