Similar to "faced":
* Encountered
* Confronted
* Experienced
* Met with
* Suffered (for negative situations)
* Endured (for difficult situations)
Similar to "underwent":
* Experienced
* Suffered (for negative experiences)
* Endured (for difficult experiences)
* Undertook (for actions taken)
* Passed through (for a period of time)
The best synonym depends on the specific situation. For example:
* "She faced her fears" could be replaced with "She confronted her fears."
* "He underwent surgery" could be replaced with "He experienced surgery."
It's always helpful to consider the context and the specific meaning you want to convey when choosing a synonym.