WASHINGTON — The Supreme Court seemed prepared Tuesday to allow Samsung to recover at least some of the nearly $400 million it had to pay Apple for incorporating into its smartphones some of the innovative design elements of the iPhone.
But the justices did not seem ready to approve lower-court decisions that said Samsung must pay all the profits from 11 phone models for violating several of Apple’s design patents. Samsung’s lawyer Kathleen M. Sullivan reminded the court that smartphones contain more than 200,000 technologies that are not at issue.
But in their first examination of design patents in more than a century, the justices seemed vexed about how to devise a test that would allow judges and juries to figure out how to compensate an injured patent holder.
‘‘It’s one thing to leave it to the jury,’’ said Justice Anthony M. Kennedy. ‘‘If I were the juror, I wouldn’t know what to do.’’
The case is one of several legal battles between Samsung and Apple over the lucrative smartphone market. It not only is important for the companies but also could have a significant impact on the high-tech industry, where design and function are key to success.
The court is trying to interpret a statute that says that a party that infringes on a design patent may be held ‘‘liable . . . to the extent of his total profit.’’ But it also says that such infringement occurs when the design patent is applied to ‘‘any article of manufacture.’’
In other words, is the patent holder entitled to all of the profits from the sale of a complex product, even if the design applies only one component? Or are the damages confined to the value solely of that design feature?
Sullivan argued that it is simpler when the product is something like the design of a carpet or of wallpaper. But Apple’s design patents on a flat rectangular screen with rounded edges and a grid of colorful icons are a small part of Samsung’s smartphone.
‘‘A single design patent on the portion of the appearance of a phone should not entitle the design patent holder to all the profit on the entire phone,’’ she argued.
But the justices had trouble drawing that line. Referring to examples in amicus briefs, they asked about something as iconic as the design of the Volkswagen Beetle and how one would determine whether the automaker would be able to collect the entire profits of a rival who copied the design.
‘‘Nobody buys a car, even a Beetle, just because they like the way it looks,’’ Justice Samuel A. Alito Jr. said.
Sullivan, the Obama administration, and even Apple lawyer Seth P. Waxman agreed that the ‘‘article of manufacture’’ could be just part of the product in some cases.
But not in this case, Waxman said.
‘‘Whatever you determine the right instruction should be, there is no basis to overturn the jury’s damages verdict in this case,’’ Waxman said. Samsung never identified ‘‘any article of manufacture other than the phones themselves.’’
Waxman said Samsung faced what one executive described as a ‘‘crisis of design’’ and decided to copy the revolutionary look of the iPhone rather than continue to lose sales to its competitor.
But Sullivan countered that the company tried to make the argument that it should be liable for only a share of the profits and was stymied by lower-court rulings.
Justice Stephen G. Breyer said those disagreements led him to think that more work was needed.
‘‘We have a hard enough question trying to figure out what the standard is,’’ Breyer told Waxman. ‘‘Now, why can’t we just ask the lower courts to listen to your arguments and theirs, and work it out?’’