Place the water in a large saucepan, add the lime and bring to a boil. Add the salmon fillets.
Reduce the heat to low and simmer covered for 10 to 15 minutes. Remove from the heat and using a slotted spoon, transfer the fish to a plate lined with paper towels.
Place the arugula, pine nuts, garlic and olive oil in a food processor and process until a smooth paste is formed.
Add the parmesan cheese, salt and pepper and process for about 20 seconds.
To serve place the salmon in a serving plate, season with salt and pepper and spoon the pesto over the top.