Let the blini cook until the bottoms are golden brown, 2 to 3 minutes. Flip and cook on the second side until golden brown, about 2 minutes.
Transfer to a baking sheet and place in the oven to keep warm. Repeat with the remaining batter.
When all of the blini have been cooked and you are ready to serve, arrange them on a serving platter. Top each with some of the smoked trout, horseradish-yogurt blend, a dollop of caviar and fresh dill.