Special equipment: 2 lollipop molds and lollipop sticks (available at kitchen specialty and craft stores). Arrange the lollipop sticks in the lollipop molds and place on a baking sheet. Set aside.
Combine the sugar, water, and cream of tartar in a heavy-bottomed saucepan over medium heat. Stir until the sugar is dissolved. Increase the heat to high and, without stirring, cook until the sugar is amber or until a candy thermometer reads between 300 to 310 degrees F (hard-ball stage), about 10 minutes (see Cook's Note*). Promptly remove the saucepan from the heat. Carefully stir in the flavored extract.
Work quickly, drop 1 teaspoon of the hot mixture into each lollipop mold. Reheat the mixture briefly over low heat if it starts to thicken. Let the lollipops cool for at least 15 minutes. Remove from molds and store in airtight containers or wrap individually.