To prepare marinade combine jam, hoisin, lime juice, coriander, ginger and sesame oil in a small bowl. Stir well.
Pour into a resealable plastic bag or glass bowl; toss tuna with marinade to coat. Refrigerate for 1 hour.
Preheat barbecue for high heat and lightly oil grate.
Remove tuna steaks from marinade, shake off excess and discard remaining marinade. Cook on preheated barbecue for 4 to 5 minutes per side Be careful not to overcook - the tuna should be lightly browned on the outside but still slightly pink in the middle. Serve immediately.