Medicare age. Retirees can first enroll in Medicare during a seven-month window that begins three months before the month you turn 65. Sign up at the beginning of this period if you want coverage to begin the month you turn 65. If you miss the initial enrollment period, you can sign up between Jan. 1 and March 31 for coverage that will begin July 1, but you will be charged late enrollment penalties for as long as you have Medicare. "Late enrollment penalties from Medicare can be long-term," says Anna Maria Chavez, chief strategy officer and senior vice president for external affairs at the National Council on Aging. "You don't want to have to worry about higher costs, just because you didn't act when you became eligible at 65." If you delay Medicare enrollment because you or your spouse is still working at a job with group health insurance, sign up within eight months of leaving the employer or health plan in order to avoid the penalty.