Amateur Radio is alive and well in the Cayman Islands, and there are dozens of active amateurs scattered around the country. The Cayman Islands has a reciprocal licensing agreement with the US, which makes it about as hassle-free a place for radio operations as I can imagine.
Licensing: This is extremely easy to do. All that is needed is a photocopy of your home license, $20CI (or $25 in US currency), and a simple application form.
There were some organizational changes within the Cayman Islands government at the end of 2002 which affected the way licenses are issued. Licensing is now handled by an agency called the "Information Communications Technology Authority". I believe they are currently located in the Piccadilly Building in downtown George Town, but believe they are planning on moving to different quarters in the near future. In any event, the gentleman who handles amateur radio licenses is Kevin Washington, and should you contact Kevin in person I believe you will find him very friendly, helpful, and responsive. When Kevin first assumed his post in January of 2003 there was an enormous backlog of paperwork awaiting him. All licenses in the Cayman Islands used to expire on the same date--January 31 of each year. Thus Kevin had renewals for all amateur licenses as well as aircraft licenses (!) and other commercial licenses demanding his immediate attention. It took him a couple of months to work through that backlog and I have no doubt there are some people who misunderstood the delays they experienced during that time. Kevin has bent over backwards to help me and the guest operators I have had visit me on Little Cayman and I have talked with other people who have had the same experience in dealing with him.
If you need to phone Kevin, he can be reached at 345-945-8283. The mailing address, which is a post office box, will not change when ICTA relocates:
Information Communications Technology Authority
P.O. Box 2502 GT
George Town, Grand Cayman
Cayman Islands, B.W.I.
When you contact Kevin for a license you will need to obtain the application form from him. He probably can send this to you via fax if you can provide him with a fax number. Then you will need to return the completed form plus a copy of your home license and the $25 USD fee. Note that the Cayman Islands government will not accept a check drawn on a US bank. However, Kevin can provide you with a form you can complete that will authorize payment on a MasterCard or Visa account. This is a lot easier than buying an international postal money order or arranging for a wire transfer!
Calls: The active prefixes in the Cayman Islands are ZF1, ZF2, ZF8, and ZF9. Only citizens of the British Commonwealth can receive the ZF1, ZF8, and ZF9 prefixes. In those cases, it is the island of residency when you first get your license that determines the prefix. People residing on Little Cayman will receive a ZF8 prefix, people residing on Cayman Brac will get a ZF9, and Commonwealth citizens either visiting the islands or residing on Grand Cayman will get a ZF1 call. Everybody else will get a ZF2 call. After the call is issued, people can (and do) move around freely without having to change their call. I know one very active ZF1 on Cayman Brac, for example.
CI Amateur Regulations: There is nothing particularly obtuse about the rules in CI. The frequency limits are about what you would expect of any IARU Region II country. The band limits are the same as in the US, except that the SSB limits are much broader: everything above 3600, 7050, 14100, 21100, 28100, and ALL the WARC bands. (Yes, unfortunately, including the whole of 30m.) The power output limit is 1KW--everywhere. (Yes, including 30m, including 7100-7150, 21.1-21.2, etc. Please spare me the lectures that don't apply in CI.)
National Society: The national radio society in the Cayman Islands is known as C.A.R.S.--the Cayman Amateur Radio Society. It's an active club, with a club station (ZF1A), a weekly net, regular meetings, and a monthly newsletter. The requirements for admission are relatively straightforward: a heartbeat and a checkbook. (A license may also be required, but I'm not sure about that.) Visiting hams are encouraged to join the weekly net. For more info, follow the above link to their web page.
Contesting in the Cayman Islands: From my experience, this is a mixed bag. It's not a particularly good location for the CQ contests because it's in 2-point land. As far as the US is concerned, it's a bit too close for the high bands. I always have a rough time getting MS, AL, GA, SC, etc. on the high bands, and particularly on 10m. I expect that problem is going to get even worse in the years to come. Of course, there's a decided LF advantage because of the proximity--but I do feel that advantage is more than offset by the HF disadvantages. Propagation to EU is extremely good on HF, but even there I think CI suffers in comparison with the eastern Caribbean because our opening to EU is much shorter than theirs. Just map out how any hours of the day 8P, J3, J8 and J6, for example, share daylight with EU and then compare that with how many hours CI shares daylight with EU. Another point worth mentioning is that there are always other contest stations--principally the club station, ZF1A--active from Grand Cayman. That has to hurt some. So if your interest is purely to construct a contest station that has a chance of taking on the HC8 behemoth, let me make a suggestion: 9Y. That overcomes all the problems I mentioned above, with the possible exception of LF to NA.