I have been on Coumadin most of my adult life, although I do NOT have an underlying cardiac condition (so my situation is different from your husband's). There are a few things I do that make me feel safer when I travel.
I joined the International Association for Medical Assistance to Travelers. It provides names of qualified English-speaking doctors in various countries; it can also answer some questions and provide other services. They may be able to provide some suggestions for your doctor about testing while you're traveling. The cost is very nominal.
I know that portable self-test devices have been developed, although I'm not sure how available they are. I'd suggest asking your cardiologist about that, and if he doesn't know, try to get an answer from a hematologist.
I carry a very good medical evacuation policy. With most medical evacuation policies, a clerk at the insurance company decides if you need to be evacuated. I use Medjet Assist, which allows me or a family member to make the decision about whether I should be evacuatEd – provided the doctors agree that it is safe. I've never had to use it, but it's worth it for peace of mind. It also will cover domestic travel, as long as I'm 150 miles from home.
I bring two times the amount of Coumadin that I will need, and I divide it and store it in separate places. That way, if one stash vanishes, I have the back up. I started doing that after my medications got lost in a chaotic security inspection. At that time, Italy only sold 5 mg tablets, which was a little challenging since my dose was 3.5 mg.
Finally, about 6 weeks before I leave on my trip, I modify my diet so it reflects what I expect to eat while I'm traveling. Typically that means reducing the amount of high vitamin K food that I eat. That allows me to adjust the dose if necessary before leaving. However, I've been doing this a long time, and my protime doesn't shift dramatically with diet; I wouldn't suggest you try it without talking to your doctor.
I hope everything works out happily – both with your husband's health and your travel plans. If you have any questions, feel free to send me a PM.