It would help to have more details (airline, destination, etc.), but generally if you miss your flight, you're best off getting to the airport as quickly as possible. Most airlines will put you on the next available flight on a stand-by basis without charging a change fee or any difference in fare, and generally you can keep standing by until you finally get on a flight without a limitation on time. If you want confirmed space on a later flight, you'd have to pay both the change fee and any fare difference.