The Japanese equivalent of underlining for emphasis would probably be using 傍点【ぼうてん】 or 脇点【わきてん】:
Dots added over (if writing horizontally) or to the right (if vertically) of each character.
Wikipedia Japan has a page detailing their use, as well as their variants:
If writing vertically, people mainly
use the "black sesame (goma)":﹅ or
horizontally, the round black (●) or
white (○) dots are preferred.
work" double-circle (◎) and bull's eye
circle (◉) are also used.
While some people differentiate between "sesame" (goma) and round signs, many people don't and use them indifferently.
(there are a couple other particular cases, such as when reporting an erratum, but I don't think you are particularly interested).
To conclude, you probably want to use the simple round black marker, like such (with slightly less distance between the lines, typically where the furigana would be):
Listen really well