Curious if this is actually the right way to store nuts, I posed the question to experts. Second best is refrigerating them in airtight glass containers.” Whether you’re using the former appliance or the latter, Montenegro suggests buying a set of Rubbermaid Brilliance Storage Containers. Moladri 28-Ounce Glass Storage ContainerAmazonSince Chef-in-Residence Robert Dahl from California Walnuts goes through walnuts so quickly, he stores them in his refrigerator. If this applies to you, she says the pantry is okay so long as you use “truly airtight” containers, like OXO Pop. If you don’t need this large set of 10, they’re also sold as single containers or in packs of three.