Wash limes hot, grate dry and cut 1 lime into thin slices. Wash the fish, dab dry. Heat the oil in an ovenproof pan. Fry fish on the skin side for 2-3 minutes. Place 2 lime slices on each fillet.
Sprinkle with some sugar and season with salt and pepper. Cook the fish in a preheated oven (electric cooker: 175 °C/ convection oven: 150 °C/ gas: see manufacturer) for 5-7 minutes.
Meanwhile cook the peas in boiling salted water for 2-3 minutes. Wash coriander, shake dry, pluck leaves and chop. Halve 1 lime and squeeze it. Drain the peas, let them drip off and put them back into the pot.
Add butter and lime juice and mash coarsely with a potato masher. Mix in the coriander and season with salt and pepper.
Arrange the pea puree on plates and place 1 salmon fillet on each plate. Garnish with lime wedges if desired.