The woman contacted police to report the items stolen after finding that they had not been handed in to security.
The force is now appealing for anyone with information to come forward.
The wedding ring is a platinum band with a single one-carat diamond, while the eternity ring has about 24 diamonds around the circumference.
A police spokesman said: "The woman has been left devastated at the loss of her rings and is desperate to have them returned to her as soon as possible. Anyone who comes into possession of the rings is asked to hand them in to their local police station.
"We would also ask that anyone who can assist with our enquiries into this theft contacts police immediately."