There is one mentioned in the top comment, St. John's.
Meaning they're still taking exams.
"The goal of the Reed education is that students learn and demonstrate rigor"
https://www.reed.edu/about-reed/history.html
Demonstrate rigor sounds like tests.
"Among the requirements for the major are successful performance on a junior qualifying examination, completion of a yearlong senior thesis based on original research or artistic expression, and a successful oral defense of the thesis before an interdisciplinary faculty board."
Testing is definitely done.
Also "demonstrate rigor" absolutely does not imply tests. In my undergrad (math) the level of rigor of tests was uniformly (and necessarily) much lower than homework and other assignments without the same time pressure. I would expect the same to be true in many other fields.
> Also "demonstrate rigor" absolutely does not imply tests.
Sure it does.