1. With meat mallet or dull edge of French knife, pound each pork cutlet to about 1/8 inch thickness. Cut each cutlet into 2 or 3 pieces. Combine flour and 1/4 teaspoon salt. Dip pork pieces into flour to coat lightly.
2. In 12-inch skillet over medium-high heat, melt 2 tablespoons butter or margarine (1/4 stick). Cook cutlet pieces, a few at a time, until browned on both sides, about 3 to 4 minutes, removing pieces to warm platter as they brown and adding more butter or margarine if needed. Keep warm.
3. Into skillet, measure vermouth, water, and 1 tablespoon butter or margarine, stirring to loosen brown bits from bottom of skillet; over high heat, heat to boiling. Reduce heat to medium; cook 2 to 3 minutes, stirring often.
4. Meanwhile, in 2-quart saucepan over medium-high heat, melt 2 tablespoons butter; add cherry tomatoes, savory, and 1/8 teaspoon salt. Cook, stirring frequently, until heated through.