How do companies keep track of what their one of a kind, highly skilled worker is doing?

The outcomes they produce, together with periodic reports and discussions.

“Workers” are performing known tasks to produce results that have been planned and calculated. So schedules, performance quotas, quality levels, output of all kinds can be monitored.

If you’re asking “How do companies know what their knowledge workers are doing?” meaning: researchers, R&D people, laboratory bosses, etc., that’s measured by… gradual (sometimes precipitous) and continual improvements in products or production methods for the aforementioned production.

I interpret this question as “How do you know when your employee is wrong when you don’t fully understand what they’re doing”. A few things come to mind:

1. People like this usually work on teams. You’re never gonna have 1 guy designing the entire rocket. You’ll have lower level people cranking out calculations that advise decision making on a bigger picture, of which upper level people are leading. Thus a system of checks and balances of sorts.

2. Some technical people work alone, e.g. some engineers although many engineers also work on teams. These guys go through a licensing process. Sometimes the things they design are peer-reviewed. Sometimes the things they design get built then maintained – the owner hires other engineers to assess the condition of what was built. Sometimes things get built and subsequently fail – no one caught the mistake until it was too late. Sometimes in this case, engineers are hired to investigate why.

3. In academia, people publish their work in peer-reviewed journals, which means their research/work is picked apart by their peers before it gets published.

In the “real”/corporate world, I imagine a business owner is either technically competent in his business or has someone who is as an interface between him/her self and the technical staff.

They have to give a high level explanation of what they are doing. Then they have to demonstrate that it works, or if it doesn’t work, be able to explain what went wrong.

Having a genius one of a kind employee is only worthwhile if you can take advantage of their expertise by bringing something to market.

Test demonstrations.
The scientist guy at Oscorp in Spiderman messed up in making a super-soldier serum. This ticked off his boss Norman Osbourne, who promptly tried the serum and became THE GREEN GOBLIN!

Nowadays knowledge workers receive objectives and most decisions how to achieve them are taken by the knowledge workers themselves, not by the superior or someone else in a company. This approach fosters employee empowerment and increased satisfaction, and is the exact opposite of “keeping track”. Only very few employees require micro-management and in such cases it would have been better not to hire them in the first place.

There should be regular 1:1s with all direct reports, which offers employees to raise issues. It is one of the most powerful management tools available.

My husband is given quite a bit of leeway. He’s not strictly an inventor any more so his work is more task based. He travels the world and fixes things so oil rigs don’t fail and ships don’t crash. His mangers have to have faith in him that he’s not wasting time and that his outcomes are the best for the customer and the company. The managers don’t know how to fix the equipment and have it successfully integrated with the masses of other equipment based on the rigs and ships, and neither to the captains or the drilling companies. Before he leaves a job, he has to provide a report to satisfy the company he works for and the ship’s captain or rig management and he has to show that the equipment now works… or what has to be done as far as replacement and upgrades go and a time and plan schedule for that.

He hates reports, but he has gotten good at them. He’s also had to become more patient at explaining things and liaising with people who have no clue or become very controlling and rude. He has to manage this in several languages, many of which his managers don’t speak.

They do give him some leeway, as I said. Because of the travelling he does, he can add a day here or there and play tourist, or he’ll end up playing tourist while he waits for a part or a key person to arrive or some key work to be finished. As long as he gets the job done and doesn’t add several days of sitting on his arse with lodging and expenses for no reason, they leave him to it.

The people who control the money strings will certainly have a handle on what they expect, you can be sure of that. They want their pound of flesh.

Like any other worker. They are a part of a much bigger thing.
Just because you aer empowered or entrusted to do things at a higher level does not mean you are monitored more or less.
If anyone does not perform as the task or job requires, it is noticed. As others have listed here, deadlines, periodic meetings, observed progress on tasks, feedback, the keystroke monitor on your PC, if something blows up, the little camera in the corner, etc…...
Most organizations work on the core principal that people are doing their job and that peers and supervisors and team will notice if they are not.
There are plenty of ways to monitor poor performers once a person is suspect of such.