Try text messaging on your mobile phone. A text message may get through even when the voice component of the cellular network is congested. Short text messages are sent via the cell-site control channel, which is always available, rather than over the limited number of voice channels available for telephone calls.
Making use of email and social media sites are also part of a good emergency communication plan. You can predefine who you want to contact with your status. In recent disasters, these methods have proven to be excellent ways to communicate.
The use of "out of area" contacts is another effective way to communicate. Although local phone systems may be tied-up after a disaster, long distance circuits are often unaffected and can be used effectively to check on your loved ones.