Prepare an ice-water bath. Heat sugar and the water in a heavy saucepan over medium heat, stirring occasionally, until sugar is dissolved and syrup is clear. Stop stirring; cook until syrup comes to a boil, washing down sides of pan with a wet pastry brush to prevent crystals from forming. Continue to boil, gently swirling occasionally, until medium amber. Plunge pan into ice bath to stop the cooking; let stand until thickened, about 10 minutes. (To test: Dip a skewer in caramel and lift a few inches; if a thick drip slowly forms and holds a string, the caramel is ready.)
Dip a skewered hazelnut into caramel, letting excess drip back into pan. When dripping syrup becomes a thin string, secure opposite end of skewer under cutting board. Repeat with remaining hazelnuts. (If caramel hardens before all hazelnuts have been dipped, rewarm it over low heat.) Let stand until caramel string has hardened, about 5 minutes; break each string to desired length. Carefully remove skewers. Candied hazelnuts should be used the same day; store, uncovered, at room temperature until ready to serve cupcakes.