Uncharted territory
It is be very difficult to measure intelligence on very smart people. At least the "400 IQ" would be hard to be differentiated from a "200 IQ".
The first hurdle is translating one's intelligence to a number. You can do that with IQ, however, note that it is a test built so that, if one measures a population, the result is(or should be close to) a normal distribution of with average 100 and standard deviation 15.
A Normal distribution is concentrated around its average, it is symmetric: half of the population should have an IQ higher than 100. Furthermore, the proportion of people in a given interval is fixed, 15.8655% of a population should have some measure higher than the average plus 1 standard deviation. 964
In our case, 15.8655% of the population should have an IQ higher than 115. You can consult a table here that, among other things, says, for number of standard deviations(Wikipedia refers to it as z), the proportion of the population with an measurement higher than avg + std * z.
According to Wikipedia(just googled "word population"), as of March 2020, there are around 7,800,000,000 people in the world, with that amount of people, there should be 7 or 8 geniuses in the world with an IQ higher than 190 - 6 standard deviations, so 9.86588E-10 * 7,800,000,000 is the expected value of people with IQ higher - note that the proportion under a region falls very fast as it gets farther from the average. The chance of someone having an IQ higher than 215 is 1.27981E-12, that is 770 times less likely, so it expected that 1 person in all people who have ever lived(estimates around 50-150 Billions).
Note that 400 is 20 standard valuations, this is chance of that happening is 2.75362E-89. Even if every atom in the universe(estimates from 1E+78 to 1E+82) had an IQ that followed human distribution, it still would be hard(1E+82 * 2.75362E-89 = 2.75362E-7) to find an atom with an IQ higher than 400.
The best one can do
If your guy has 400 IQ or more, the best thing one can do is to find a way compare them with the smartest people ever. Then they will know your guy's IQ is at least 190.
Scored 190 while reading a novel and reading the test backwards
Perhaps try handicapping: they could make the person try multiple "tests"(competitions with the best) at the same time, maybe try it in different languages(as suggested by other people), have the test be written backwards and make your character write it with inside-out alternating order(so 1,2,3,4,5 becomes 3, 4, 2, 5, 1), or some other ridiculous thing. 840