It can be asserted in a civil matter to protect you from criminal prosecution, but it is still subject to civil penalty.
Also, groundless claims of 5th amendment privilege are subject to contempt.
Here, this was a civil divorce. I don’t see what criminal prosecution she could face. She just didn’t want to admit she was banging some 18 year old.
Thanks, all. I could not click the link (for some reason!), and got confused between the custody part and the woman’s fooling around part; where she was pleading the Fifth, etc. So, I didn’t know what she held in contempt of.