1. To greatly increase the cost or scarcity of something. Because the city is so densely populated, landlords are able to put a premium on rented accommodation.

2. To place an especially high value on something; to consider something more important or valuable than is usual. We always put a premium on our customer service support, so never hesitate to contact us if you have a problem. With three young children, I put a premium on a shop where I can find everything I need in one stop.