I have a colleague who got divorced and it had to go to trial. The colleague's ex-wife was lying so badly on cross-examination that the judge ( a woman) stopped the lawyer and explained to the ex-wife that she really had to try to tell the truth because she was under oath.
The ex-wife was incredulous. She angrily asked the judge how she could be expected to tell the truth when her husband was trying to take away not only their kids (he was applying for joint custody) but her undoubted right to a huge amount of lifetime alimony (they had been married 6-7 years). The ex-wife thought her ex-husband's positions were so outrageous that justice allowed her to do anything to defeat them, including lying under oath.
The judge then again begged the ex-wife to concentrate on telling the truth, but obviously that instruction was so ridiculous that the ex-wife immediately ignored it and went back to lying. (I couldn't believe the story when it was told to me, so my colleague gave me a copy of the transcript and sure enough that is exactly what happened.
No perjury referral, of course, though the ex-husband did get joint custody and alimony stopped after a while.
As they say, family court is where the law goes to die.