Thomas Massie

After Representative Thomas Massie, an outspoken Republican critic of President Trump, lost his seat in a closely watched primary last week, he brushed off questions about his future political aspirations by saying he was going to run — back to his off-the-grid Kentucky farm.

But as Mr. Massie pondered his future, and recovered from the most expensive House primary in recent years, he set a heading this week for sandier horizons, flying to Costa Rica. Waiting for him when he landed was a familiar Trump antagonist from the Republican Party: former Representative Marjorie Taylor Greene of Georgia.

Ms. Greene, who maintains a house in the Central American country, arrived there earlier this month for a two-week birthday trip, her fiancé, Brian Glenn, said in an interview. In recent days, Ms. Greene invited Mr. Massie and his wife, Carolyn, to hop a last-minute flight to join them at the house, and the congressman arrived on Tuesday, Mr. Glenn said.