Set oven rack about 6 inches from the heat source and preheat the oven's broiler.
Lay crackers salt side down on a baking sheet. Spread tomato paste on top.
Microwave sausages in a microwave-safe plate until heated through, about 1 minute. Slice in half lengthwise, making sure not to cut all the way through. Place sliced side-down onto the crackers. Quarter each slice of cheese and lay over the sausage.