Radiation-curable compositions, and methods of making the same, for providing a wide variety of substrates with a durable, colored coating or colorant are disclosed. The color is at least in part provided by chromophore molecules that are covalently bonded to other components within the radiation-curable composition. A telecommunication element having a durable color identifying polymeric coating thereon is also disclosed. The telecommunication element comprises an elongated communication transmission medium, such as an optical fiber or an optical fiber ribbon, and a radiation-cured polymeric coating having an identifying color applied on at least a portion of the transmission medium.