If you miss the Initial Enrollment Period (IEP), you can still sign up for Medicare during the General Enrollment Period which runs from January 1-March 31. People who sign up during the General Enrollment Period will be eligible for coverage the following July. Late enrollment penalties typically apply for people who miss their Initial Enrollment Period. Depending on the Part of Medicare that you apply for, these penalties can vary from 10% for every 12 months you delay enrollment or 1% per month.