You will find a good selection of recognisable brands of underwear and lingerie in shops on-Island.
There are a few shops in Grand Cayman which sell lovely sets of underwear and bras, and there are experts in those shops who can properly measure and fit you for a bra. Vy's Closet offers bra-fitting services at a rate of CI$30 for 30 minutes, and the fitting fee is waived if you purchase a bra. The nice thing about buying underwear and lingerie locally is that it suits the climate.
There is a dedicated lingerie shop in Camana Bay called Silhouette, and there is also Atlantic Department Store which can be found in Paddington Place off Godfrey Nixon Way, which has a wonderful selection of underwear and is especially set up for teens and the fitting of their very first bra. They also stock a good selection of cool, light pyjamas and nightwear.