I first came across this tip over on Ann Drake’s blog here. It seemed too simple not to try. All you have to do is mix a little bit of baking soda and water together. Slowly add the water so the mixture maintain a paste consistency. If it is too watery, it will run right off the silverware.
Place some of the paste on the affected spots and rub with your finger. Wash off the silverware to check the progress and repeat the process as necessary. After a few cycles the rust spots should be all gone!