Apple (Nasdaq: GOOG) is told to pay $368 million in a patent suit about video calling technology, and Google (Nasdaq: GOOG) as well as AOL lose a patent case about search engine ad patent in court decisions disclosed Tuesday.

Apple vs. VirnetX Case

VirnetX Holding Corp. was awarded $368.2 million after a federal jury yesterday said Apple Inc. infringed its patents for virtual-private-network technology used in Apple’s FaceTime video-calling function.

VirnetX, which won a $200 million settlement from Microsoft Corp. in 2010, accused Apple of infringing four patents related to private networks. The case targeted Apple’s iPhone, iPod Touch and iPad as well as Mac computers that use the FaceTime function. Apple denied infringing the patents and contends they’re invalid.

The VirnetX patents cover the use of a domain-name service to set up virtual private networks, through which a website owner can interact with customers in a secure way or an employee can work at home and get access to a company’s electronic files. VirnetX had sought $708 million in damages.

“For years Apple refused to pay fair value for the VirnetX patents,” Doug Cawley, a lawyer with McKool Smith in Dallas who represents VirnetX, said in closing arguments. “Apple says they don’t infringe. But Apple developers testified that they didn’t pay any attention to anyone’s patents when developing their system.”

Following the verdict, Cawley said VirnetX would seek an order to block further use of its inventions. Kristin Huguet, a spokeswoman for Apple, said yesterday the company had no comment.

The focus of the trial before U.S. District Judge Leonard Davis was on Apple’s FaceTime, which lets people use Mac computers to make video calls to an iPhone, iPod Touch or iPad. The Cupertino, California-based company said it used a different technology than what was covered by the VirnetX patents.

“Apple does not owe money to VirnetX,” Danny Williams, a lawyer with Williams, Morgan & Amerson in Houston who represents Apple, told the jury. “VirnetX is not entitled to money for things they did not invent. The VirnetX technology, if used, is a small part of very large, complex products.”

The case has received so much attention that Davis ordered the parties on Oct. 19 to tell their investors to stop calling the court. He said in a court filing that his office is receiving more than 10 calls a day.

The technology stemmed from work performed by SAIC Inc. for the U.S. Central Intelligence Agency to develop secure communications, VirnetX has said. VirnetX, based in Zephyr Cove, Nevada, was formed by former employees of SAIC, which was named as a party in the complaint though isn’t participating. According to VirnetX regulatory filings, McLean, Virginia-based SAIC may be entitled to a share of any verdict or settlement.

Vringo vs. Google, AOL

Vringo Inc., owner of technology developed by the Lycos Inc. search engine, said it was awarded about $30 million from Google Inc. and some Google customers, including AOL Inc., over patented ways to generate advertising revenue.

The companies infringed two patents owned by Vringo, a federal jury in Norfolk, Virginia, decided today. Vringo said it was awarded a 3.5 percent continuing royalty rate on the patents, which expire in 2016.

Vringo claimed Google’s Adsense program, which is also used as the advertising platform for third-party companies and AOL Search Marketplace, infringed the patents. The company had been seeking $493 million, before U.S. District Judge Raymond Jackson ruled that Vringo couldn’t collect any damages that might have occurred before the suit was filed in September 2011.

“We remain confident that the patents here are invalid, that we did not infringe them, and that we will ultimately win this case,” Google attorney Catherine Lacavera said in a statement.

Google was told to pay $15.8 million, AOL $7.94 million, and IAC Search & Media Inc. $6.65 million, Vringo said in a statement. Target Corp. was told to pay $98,833 and Gannett Co. $4,322. The companies all use Google’s program to display ads based on search results.

Jackson still has to rule on one validity issue, and both companies are expected to file post- trial arguments, Vringo said.