The LIGA technique (LIGA is a German acronym) is a type of
micromachining. I am seeking a list of U.S. companies that do LIGA
micromachining. I am not interested in government or academic
laboratories or foreign companies.

Hi dgc-ga, 
  
I've found the (very) short list of U.S. companies that perform
lithography electroforming and molding.
In 2000, there was only one company doing so: AXSUN Technologies
licensed LIGA technology from Sandia National Labs.
A press release is available here:
"News Release - MEMS Technology", Sanda National Labs
http://www.sandia.gov/media/NewsRel/NR2000/mems.htm
AXSUN Technologies' home page:
http://www.axsun.com/
Another company has started doing LIGA micromachining in the U.S.
according to the MEMS Clearinghouse:
"Mezzo Systems Announces Availability of LIGA Foundry Services", MEMS
Exchange 2002
http://www.memsnet.org/news/982818000-5/
Mezzo Systems explains their LIGA system here:
"LIGA", Mezzo Systems
http://www.mezzosystems.com/liga.htm

Good luck with future searches!   
   
Hoping I was helpful,   
not_you-ga

A timely and complete response to a tough research problem.