MIAMI BEACH, Fla.—Ask Thomas J. Herzfeld about Cuba, and the usually low-key money manager launches into a sermon he has delivered many times.

The 67-year-old Mr. Herzfeld says the country, under a U.S. trade embargo for 50 years, is the investment opportunity of a lifetime. And his mutual fund, Herzfeld Caribbean Basin, is ready to capitalize when the restrictions are lifted, focusing on stocks that he thinks will benefit from Cuba's opening.

Until...