While it's certainly okay to run out to the market or do errands in a casual cotton sundress, if you're putting on a summery white dress to go out, you certainly need the right accessory.
For summer, sea themes are always classic, whether it's silver and gold in the shape of seashells, or actual objects from the ocean made into jewelry. This Mother of Pearl necklace has a natural pearlescent shimmer, and would go perfectly with any neck and shoulder baring dress or top. It is available from the MOMA online store for $375.