In a small bowl, combine the mayonnaise, splash of lemon juice and a dash of paprika. Set aside.
Using a pastry brush, butter each slice of bread on one side, and place the slices, buttered side down, on a work surface. Top each of these slices with Cheddar cheese, tomatoes, argula, mayonnaise mixture and preserves. Top with the remaining bread slices, buttered side up.
Lightly butter and heat a griddle, heavy skillet or Panini press until hot. Place 2 sandwiches in the skillet and weight with another heavy pan or skillet. Brown slowly on one side for 2-3 minutes before turning, with a spatula, and grilling the other side until brown and cheese melts. It may be necessary to add a bit of butter to the skillet.