Real Tonga has flights between Nuku'alofa and 'Eua once or twice daily except Sunday.
Two boats shuttle between Nuku'alofa and 'Eua. In general, the boats leave 'Eua Monday, Wednesday, Friday, and Saturday at 0530, departing Nuku'alofa's Faua Jetty for the return at 1230 on Tuesday, Thursday, Friday, and Saturday. Ask about departures from 'Eua on Monday, Wednesday, and Friday at 1500.
Due to the action of the outheast trades, the four-hour boat trip is far less rough westbound than eastbound, so if you're a terrible sailor you might want to fly over from Nuku'alofa and catch the boat back.
The harbor at 'Eua is less secure than the one at Nuku'alofa, so if strong winds are blowing or a hurricane warning has been issued for anywhere within a thousand km, that day's ferry trip will be canceled and the boat will remain tied up at Faua Jetty in Nuku'alofa. Of course, this happens more frequently during the southern summer (Dec.-April), but one should always be prepared to spend a day or two longer on 'Eua than planned or be willing to fly back.
The Saturday trip from Nuku'alofa is the most likely to be canceled in bad weather, so it's safer to go over on Friday and not count on being able to come back on Monday. When the boat is canceled, the airline schedules additional flights.