To store rosemary, rinse the sprigs under cold running water and pat them dry with a paper towel. Gently wrap the rosemary sprigs in a damp paper towel or kitchen towel, and place them in a plastic bag or container. Store the rosemary in the fridge, ideally in the crisper drawer, and use it within 1-2 weeks. Another way to store fresh rosemary is to put the sprigs in a jar or vase filled with water, as you would with fresh flowers. Keep the jar or vase in a cool, dark place and change the water every few days. You can also dry rosemary for long-term storage. Tie a bunch of rosemary sprigs together and hang them upside down in a warm, dry place with good air circulation. Once the rosemary is completely dry, remove the leaves from the stems and store them in an airtight container in a cool, dark place.