The case under review began in 2010 when the smartphone makers filed patent infringement lawsuits against each other.
The companies have filed dozens of such lawsuits around the world to protect their technology. Apple, in particular, argues that Android phones made using Google software copy elements of its iPhones.
In the case, Apple accused Motorola Mobility, which has since been bought by Google, of infringing four patents. Motorola accused Apple of infringing a standard essential patent, one necessary to making a mobile phone work.
The cases were consolidated at the U.S. District Court for the Northern District of Illinois. Judge Richard Posner, who took the case, dismissed it in June before trial, saying that neither company had sufficient evidence to prove their case.
Motorola Mobility filed an appeal that the case be reopened. The Federal Circuit appeals court may take days or months to issue a decision.
In Wednesday's hearing many of the questions from a three-judge panel focused on whether the companies had worked hard enough to hammer out deals to license each others' patents, or whether one or the other was an "unwilling licensee."
In legal parlance, an "unwilling licensee" is a company that will not seriously negotiate paying to license a patent that it infringes. Such a company can face an order banning the sale of products that use that patented technology.
Judge Sharon Prost asked about Apple's willingness to pay to use the Motorola Mobility patent. Attorney Joshua Rosenkranz, who spoke for Apple, argued that Apple was not an unwilling licensee but that Motorola Mobility was asking Apple to pay 12 times what it had previously been paying to license the technology.
"If this court does remand (the case), I ask this court to remand with a standard," said Rosenkranz, saying that an unwilling licensee should be defined as a company that has been legally found to have infringed but still refuses to pay.
The two sides also haggled over the use of expert witnesses. Posner had excluded one Apple and two Motorola Mobility experts.
If the case is reopened in whole or part, a company or the companies can proceed with suing each other in lower court, depending on the ruling.
In afternoon trading on the New York Stock Exchange Apple shares were down 4.9 percent at $470.25 after a tepid response to the launch of its new iPhone "5C," while Google shares were up 0.5 percent at $893.50.
The case at the U.S. Court of Appeals for the Federal Circuit is Apple Inc v. Motorola, Inc and is No. 12-1549.
© Thomson Reuters 2013