Original Medicare does not cover costs that are incurred during travel outside of the country, but you can select a Medigap plan that does. Plans C, D, E, F, G, H, I, J, M and N all cover a portion of your foreign expenses. If you need emergency care within the first 60 days of your trip, your Medigap plan will cover 80 percent of the costs. Most plans will also pay for medically necessary care after you have met a pre-established deductible.