A pre-purchase survey has three parts, which BoatUS lists as the in-the-water survey, the haul-out and a trial run. The sea trial is the run. It's where the boat shows what a static inspection can't: an engine that won't reach full revs, or a vibration that starts at 1,800 rpm.
The late surveyor David Pascoe's sea trials ran at least an hour, longer on larger yachts.
What a surveyor watches
A cold start, if the seller hasn't warmed the engine first. Full revs reached against the maker's rating. Temperatures and pressures under load, and the exhaust for smoke and water flow. Steering and controls, and the stuffing box or shaft seal underway. On a sailing yacht, the rig and sails under sail if the weather allows. Back at the dock, the engine room again for leaks and heat.
On a motor yacht, an engine surveyor usually joins for this part.
In the report
The conditions and the readings by engine and rpm, then what was found. "Sea trial in 10 to 15 knots, flat water. Port engine reached 2,950 rpm against a rated 3,000. Coolant temperature steady at 82°C." See the sea trial report template.