Place the eggs into a saucepan in a single layer and fill with water to cover the eggs by 1 inch. Cover the saucepan and bring the water to a boil over high heat.
Remove from the heat and let the eggs stand in the hot water for 15 minutes.
Drain. Cool the eggs under cold running water. Peel once cold. Halve the eggs lengthwise and scoop the yolks into a bowl. Mash the yolks with a fork.
Place the tomatoes, cut sides down, onto a paper towel to drain.
Mash the cream cheese with a spoon in a bowl until smooth and workable; stir in the egg yolks, salmon, mayonnaise, brown mustard, sour cream, lemon juice, pickle relish, lemon peel, and 1 teaspoon of smoked paprika until well combined. Season with salt and pepper.
Spoon the salmon mixture into the egg halves and cherry tomato halves.
Sprinkle with additional smoked paprika for garnish and arrange on a platter. Chill at least 1 hour before serving.
