It seems like a common situation where this skill would be useful and is often lacking is where one person is an expert or semi-expert on a subject, but lacks conscious awareness of their criteria for expert decision-making. A concrete example of this that I have experienced is trying to explain to someone how I know confidently and in an instant something like "that tree is a kind of maple" or "that bird is a robin". Asking me this forces me to step back and start pointing out all the information I'm taking into account, which usually turns out to be possible, but surprisingly challenging.
The trouble with constructing an exercise based on the expertise of the student is that everyone's knowledge is idiosyncratic. And, with wide-speared knowledge, somebody usually has to pretend to be ignorant. I've seen an exercise used at job interviews, where they have the applicant "describe to a blind person how to tie shoelaces" (someone below had seen "teach me to sharpen a pencil", which has the same problems); I think that requires too much role-playing to be valid, although you could use an unfamiliar knot. A good exercise should never require anyone to fake ignorance. What I would like to see tested is an exercise where participants have to collaborate to win a game, rather than play-act at it.
So I would pick some totally arbitrarily domain of knowledge. I've personally spent a lot of time using field guides, so I have an opinion about that, but you could conceivably use anything with a ready-made compendium of information.
So, two participants are separated by a wall, such that they can hear each other perfectly, but not see each other.
Person A is presented with an organism (or several photos thereof) they are unlikely to have spent much time looking closely at (which, trust me, is usually just as good as something they have never seen before). Better still, if you have time, person A is shown a group of similar organisms. Personally, I'd just use weeds you find outside of the office, because they are free and no one ever looks at them closely. Person A also gets a ruler and magnifying glass (and, if it were up to me, several completely useless items to keep them from fixating on any one in particular).
Person B gets all the reference materials. (I'd be curious to see how it worked with and without a dichotomous key, and with photos vs. field marks, if those are options.) Together, they have to work out what Person A is looking at, or get as close as they are able, and say specifically why they arrived at their conclusion.
In order to win the game, you can't just say "it has a thingy" or "it's red" -- you have to be able to explain how you know what you know, and you are forced to arrive at a mutually intelligible vocabulary. I will caution that this will be an insanely difficult exercise for some people, and they might need some incentive to not give up too easily. I think it has to be hard in order to not seem excessively contrived.
The potential failure mode here is that any skills gained wouldn't generalize, even if the game really does require communicating concretely in order to win. I would definitely not expect people to be immediately better at pitching a start-up afterwards, but the hope is that they would come away with the experience of what it feels like to communicate concretely about a domain of information they have access to.
I'd love to test this on my own friends, actually, but I think they'd kill me.