Job search when coming up for tenure I notice that coming up for tenure/getting tenure is often an opportunity to move to another institution (even if tenure is granted). How does this work in practice? Is it common for assistant professors to formally go on the job market the year that they are up for tenure? Do they do it only informally, by asking around? Do schools just make offers to up-for-tenure APs without prompting? 

I'm curious how this works, because it seems that often times these moves are worked out shortly after tenure decisions are made, so it seems like they must have been in the works before hand. 

I'm most interested in highly ranked US based research universities.
This is a manifestation of game-playing, and is completely understandable once one starts thinking in such terms.

For example, if a person is in an excellent situation to get tenure at their current institution, they are probably in an equally good position to get other jobs, perhaps with tenure.

Another feature: if a person has done good-enough work that they've got outside offers, this can set in motion the getting-tenure process at their current institution.

(Shallowly enough, the "best" certification of one's academic virtue is outside offers.)

At the same time, I think most up-for-tenure assistant profs in the U.S. are not really looking for outside offers as they come up for tenure, so even if they could generate them, they'd not try. For that matter, despite the "rewards", many people find this game-playing obnoxious so don't do it.

To answer another part of your question: yes, most formal job offers only arise after informal inquiries and back-and-forth, because... as with high-school dating... getting turned down is embarrassing. :)

The people who are interested in gaming the system continue to do so after tenure, typically...