Usually on run-up you want to check the response of the motor when changing for example the carb-heat (if existent). At least we did so on my intro flight (yey!). To prevent us from rolling onto the active runway we (obviously) held the brakes.
Now I wondered how pilots of floating planes and flying boats prevent movement on pre-takeoff checks. Additionally most images I found from flying boats they usually have more than one engine. Similar question here: How do pilots prevent swimming circles as one engine is started and the other(s) is/are not?
I scanned this FAA document from this related question but that is mostly is about landing (which is interesting as well but I assume that as in the linked question the airframe and especially the water resistance take care of that).
