When Karen Schirack, 67, slipped on her way into her house in January and broke her left femur in multiple places, she had a decision to make. Should she get surgery to repair the fractured thigh bone and replace her hip near Ajijic, Mexico, where she has lived for 20 years, or be airlifted back to her home state, Ohio, for surgery and rehabilitation?

As the number of American retirees living overseas grows, more of them are confronting choices like Ms. Schirack’s about medical care. If they were living in the United States, Medicare would generally be their coverage option. But Medicare doesn’t pay for care outside the country, except in limited circumstances.

Expatriate retirees might find private insurance policies and national health plans in other countries. But these may not provide the high-quality, comprehensive care at an affordable price that retirees expect through Medicare. Faced with imperfect choices, some retirees cobble together different types of insurance, a mix that includes Medicare.

That’s what Ms. Schirack has done. She pays about $3,700 annually for an insurance policy through Allianz that covered her surgery at a private hospital in Guadalajara, about an hour from Ajijic. She also has a medical evacuation policy that would have paid for her flight to the States, if she had opted for that. That policy costs roughly $3,000 for five years. And she pays for Medicare Part B, which she can use for care when she visits family in the United States. (The standard Part B premium is $135.50 monthly.)