(Reuters) - Lawyers for Theranos founder Elizabeth Holmes and company President Ramesh "Sunny" Balwani on Tuesday urged a federal appeals court to overturn their convictions for defrauding investors in the failed blood testing startup, which was once valued at $9 billion.

Amy Saharia, Holmes' lawyer, told a three-judge panel of the 9th U.S. Circuit Court of Appeals in San Francisco that Holmes believed she was telling the truth when she told investors that Theranos's miniature blood testing device could accurately run a broad array of medical diagnostic tests on a small amount of blood.

Holmes, who started Theranos as a college student and became its public face, was indicted alongside Balwani, her former romantic partner, in 2018. The two were tried separately in 2022, and sentenced later that year to 11 years and three months, and 12 years and 11 months, respectively.

Saharia said the trial judge improperly allowed former Theranos employee Kingshuk Das to testify as a scientific expert about Theranos's product without making him face cross-examination about his qualifications.

She also said the judge should have allowed Holmes to introduce more evidence attacking another key prosecution witness, Theranos's former laboratory director Adam Rosendorff, including details of a government investigation of his work after leaving Theranos that she said called his competence into question.

Those mistakes could have made the difference in the "close" case, in which jurors were not able to reach a verdict on most counts against Holmes after seven days of deliberations.

Assistant U.S. Attorney Kelly Volkar, arguing for the government, disputed that Das had improperly testified as an expert, saying he was called to talk about his personal experience at Theranos. She also said that "it was not really contested that the device did not work."

The judges had skeptical questions for both sides, and did not clearly indicate how they would rule. Circuit Judge Ryan Nelson said that, even without the disputed testimony, "there was, it seemed to me, pretty overwhelming evidence."

Circuit Judges Jacqueline Nguyen and Mary Schroeder said that much of Das' testimony concerned what he observed at the company, not his scientific opinions, as Saharia argued.

Nguyen and Nelson, however, also both told Volkar that they had concerns about what opinions Das was allowed to give during the trial.

Jeffrey Coopersmith, Balwani's lawyer, argued that prosecutors had gone beyond what was in the indictment against his client by introducing evidence that the commercial testing technology Theranos secretly used was not reliable.

The judges appeared more skeptical of that argument, though again did not clearly signal how they would rule.