Spoon yogurt onto several layers of heavy-duty paper towels; spread to 1/2-inch thickness. Cover with additional paper towels; let stand 5 minutes. Scrape into a bowl using a rubber spatula; cover and chill.
Place salt and potatoes in a saucepan. Cover with water; bring to a boil. Reduce heat, and simmer 20 minutes or until tender. Drain and return to pan. Cook 10 minutes over low heat, shaking pan frequently. Cool potatoes.
Cut a 1/4-inch-deep X in top of each potato, squeezing each potato to reveal pulp. Top each potato with 1 1/2 teaspoons drained yogurt and 1/4 teaspoon caviar.