Preheat the grill over medium-high direct heat. Oil the grill grates. Finely chop the coriander and spring onions and mix in the oil and ginger. Season with salt and pepper.
Cut two 3-inch long slits through the skin lengthwise on the bottom of the salmon fillets, going about halfway into the salmon. Evenly stuff the slits with the herb mixture. Season the fish with salt and pepper.
Stir together the lime juice, soy and honey until smooth. Place the salmon, skin side up, on the grill and cook until well marked, 3 to 4 minutes. Turn the salmon and continue to cook, brushing the tops with the sauce, until the fish is cooked through, about another 3 to 4 minutes. Transfer to a serving plate and sprinkle the tops with the sesame seeds. Serve with edamame and lime wedges.