Where can you find a buyer for a 1955 double strike penny?

First off, before you have anyone buy your penny, it is going to have to be certified by a third party grading company such as NGC or PCGS. They will grade the coin on a scale from 1 being very poor, to 70 being absolute perfection. They also will note if you do have a genuine 1955 doubled die cent. This costs about $50 or so, and most coin dealers can help you with the submission process. Once you have the coin certified, there are a few options. One is to sell the coin online on an auction site like eBay, another is to go to a coin show and see if any dealers there want to buy it, and the final major option is to have an auction house auction it off for you.