years ago i travelled with my two kids alone (DH had to stay here that summer)....it was only a year after a major illness of mine, so i was very very very nervous that something would happen. My kids were 10 and 8 at the time..
i had them each wear a very small belly pack - in each pack i had a list of contact names and numbers - how to call their dad overseas from any phone; the name and number of the travel health insurance company (in case i had another attack, which was still a major worry for me at the time); all the contact names and phone numbers of relatives in the US, etc.
I went through the list with both of them before we left so they both knew exactly what to do in case of emergency.
Fortunately, they never had to use any of the information, but it was the only way i would travel with them by myself at the time.