Anuja Agrawal jumped on the phone.President Obama had just announced that he would restore diplomatic relations with Cuba — and Ms. Agrawal, who runs a medical tourism company in Orlando, Fla., did not want to miss her opening.

She reached a health care administrator in Cuba, agreeing to move ahead with a deal that they had been discussing for months in the hope that American patients could soon start traveling to the island for medical treatment.

“There was a lot of excitement about it,” said Ms. Agrawal, the chief executive of Health Flights Solutions, adding that if Americans start traveling to Cuba for affordable medical treatments, it could mean a big economic boost for the country’s health system. “For them, they’re looking at it literally like winning the lottery.”

As the Obama administration chips away at the economic isolation of Cuba, whittling at an embargo that is older than most people on this island, industries of many kinds are trying to figure out what the easing of tension will mean for them, and exactly how much wiggle room there will be.

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