You will find that Ometepe Island, besides being a tropical paradise, is extremely safe. But occasionally accidents do happen, our health doesn't always wait for our vacation to be over, and unfortunately crimes of opportunity can happen anywhere.
We highly recommend never leaving any valuables unattended. Should you find yourself a victim of theft, the most common (although still rare) form of crime on Ometepe Island, you should immediately contact the local police. This number is for the central station in San Jorge 2563-3732. They do have offices on the island and at the ferry port in Moyogalpa as well.
If you are seeking medical care; Ometepe Island offers 2 hospitals, many mini-clinics, many natural medicine and natural healing centers, tons of pharmacies, specimen labs, the works! You can get nearly everything taken care of without leaving the island.
However all of these businesses, even the two hospitals, are only open 'regular' hours. Meaning that if you have an issue in the middle of the night, your limited, but not totally out of luck. You can knock on the door of nearly any pharmacy and they will open to help you all hours of the night. Many of the local doctors will offer their private number to contact them in emergency, and there is a small boat at the lancha port in Moyogalpa that will run emergency runs to San Jorge at any hour. And worst case scenario they will call in a helicopter to you.
Things do work differently here when it comes to medical care. If you have an ailment, you walk into the pharmacy and tell them what is wrong. If it is minor they will just hand you the meds you need and send you out the door. If it requires a bit more 'expertise' they may choose to call a doctor (this will cost you about C$70) explain your symptoms, and the doctor will prescribe medications right over the phone, and may ask that you go get some tests done and follow-up with the pharmacy. You can get blood, urine, and many other specimen tests done for all less than US$5 on the island, and have the results back typically within an hour.
Many medications that are carried by the pharmacies in Nicaragua are all natural. But if you prefer to consult with a Natural Doctor, Chiropractor, or simply are looking for some natural supplements there are plenty of options for those on the island as well.