Apple faces a bill of $862m (£565m) after losing a patent lawsuit.
The University of Wisconsin successfully claimed that Apple used its microchip technology without permission in some iPhones and iPads.
The patent, filed in 1998, is said to improve the power efficiency of microchips.
The case relates to use of the technology in the iPhone 5s, 6 and 6 Plus - but an additional lawsuit making the same claim against Apple's newest models, the 6S and 6S Plus, has also been filed.
The University of Wisconsin sued Intel over the same patent in 2008. The case was settled out of court for an undisclosed sum.
In court papers, the university claimed Apple ignored its offers to license the patent, which would mean paying a fee for its continued use.
Therefore the university said Apple was wilfully infringing the patent, something which, if the court agrees, could carry a heavier fine.
The precise amount Apple may have to pay will be decided at a later stage in the court proceedings.
Despite recent well-publicised truces between some big tech firms, fierce patent battles are still being fought in courts globally.
Last week, a judge threw out claims by graphic card specialist Nvidia that Samsung and others had infringed three of its patents.