Believe it or not there are places as far as a hundred miles out in the Gulf Of Mexico where you can pick up a cell phone signal. Beware though, these signals are most likely not coming from land but from an offshore tower company that can charge you whatever they feel like. Your contract and free minutes no longer apply once you leave land.

As someone who has worked on offshore rigs for over 25 years I can say that I have seen my share of sad and angry faces when a new oilfield worker who has been using his cell phone on the rig gets his first bill.
Companies such as Petrocom and Coastel Communications, (now merged and called Broadpoint) can charge up to $5.00 per minute for calls made in the Gulf Of Mexico. I have even had their towers lock on to my signal when I was on land, such as in Venice, La, and get bills when I was not offshore.
Be aware of what system you are roaming on. Just because your phone may show "extended network" does not mean that you will not get a huge bill from Broadpoint. You must dial 611 and listen to the recording to see what company you are roaming on. 611 is a free call.

Some rigs may be equipped with a payphone that also uses one of these companies. You may be able to use a credit card or calling card in these and these phones are your best bet.
I personally use a Vonage device on my company's internet when I am offshore and avoid phones. The problem with any VOIP service like Vonage or Magic Jack on an offshore oil rig is lag time. You will hear an echo or won’t hear your party exactly when they speak due to satellite latency.
There are some new devices on the market, including Skype and Magic Jack that will work off the internet as well.
The best advice I can give you is to turn your cell phone off. You can call your voice mail from your internet phone and check it periodically.
If you do use your cell phone offshore use it very sparingly and know the rates beforehand. Broadpoint does not list their rates on their website but they will give them to you if you phone them.