If you didn’t sign up for Medicare Part B when you first became eligible, you may be able to sign up during the General Enrollment Period. This period runs from January 1 through March 31 of each year. During this time, you can sign up for Medicare Part B at your local Social Security office. If you get benefits from the Railroad Retirement Board (RRB), call your local RRB office or 1-877-772-5772. Your Medicare Part B coverage will start on July 1 of the year you sign up. --->>> Important: The cost of Medicare Part B will go up 10% for each full 12-month period that you could have had Medicare Part B but didn’t take it, except in special cases. You will have to pay this penalty as long as you have Medicare Part B.