WASHINGTON — In a case with the potential to reshape the software industry, the Supreme Court on Monday seemed poised to issue fresh limits on patents for computer-based business methods.

Though the case originated far from Silicon Valley, it has been closely watched as an indicator of how specific or abstract technical ideas can be to become eligible for patent protection. Patent claims over the way such ideas are incorporated into computers, cellphones and other devices have become a challenge for many high-tech companies.

Those companies often have interests that tug in opposite directions. They tend to hold large portfolios of valuable patents and want to protect them. But they must also contend with “patent trolls,” companies that have obtained patents on sometimes vague concepts and which are more active in the courthouse than on the production line.

Most of the justices seemed skeptical about extending patent protection to the claimed invention at issue, a sort of computerized escrow mechanism that helps ensure that both sides in a transaction do what they have promised to do.