Two South Australian jurors who researched details about an accused person in a blackmail trial have been fined $3,000 each for contempt of court.

The man and woman were jurors in a trial of three accused who were charged with blackmail allegedly committed in December 2014 at the Adelaide Remand Centre, where two of the defendants were on remand.

It was the third jury to be empanelled in the case as there had been two previous mistrials.

The Supreme Court heard that part way through the trial the judge received information that two jurors had conducted internet searches in relation to the case.

The judge then asked the jury in open court whether any members had searched the case on the internet and two of the jurors identified themselves.

In his judgment, Justice Sam Doyle said both jurors promptly acknowledged their wrongdoing.

The two jurors were dismissed and the judge declared a mistrial for a third time, after which the defendants elected for a trial by judge without a jury and were acquitted.

Both expressed contrition

Both jurors appeared in the Supreme Court after being charged with contempt of court and pleaded guilty.

"After expressing his contrition for his conduct [the male juror] explained that he had remembered the name of one of the accused 'from an incident when [the accused] was a bikie club member'," Justice Doyle said in his judgment.

"He carried out a Google search of his name which led him to find a reference on a news website confirming that the accused was the person he had remembered.

"[The juror] acknowledged that at the time he searched the internet he knew the judge had said that was not appropriate.

"[He] explained that the following morning he and [the female juror] were present with two other female jurors who were discussing why the accused had been in jail. [The male juror] told them he thought one of them was a bikie and was in jail for a 'club incident'."

The female juror also expressed contrition and said she recognised one of the accused from the news and that was why she carried out an internet search.

"She said she did not do so in order to try to sway the jury, or otherwise make a 'big scene' about it, or to inconvenience the court but she accepted, as [the male juror] said, the matter did come up in discussion over coffee with some other jurors the next morning."

The court heard both jurors were of good character and had no history of offending.

Offending described as serious

Justice Doyle described the offending as serious, especially in light of the judge's "express direction" not to do so.

"Such conduct potentially undermines the integrity of the jury system and the administration of justice more generally," he said.

"The trial process is designed to ensure that an accused is tried only on the information presented in court."

Justice Doyle said the widespread availability and usage of the internet meant information about accused people was widely accessible.

"This only serves to underscore the importance of directions, such as the one given by the judge in this case, being given, and being observed," he said in his judgment.

"Such conduct by jurors also has the very real potential, which was realised in this case, to cause a mistrial and hence occasion delay, expense and inconvenience affecting not only the accused, but also the administration of justice more generally."

Justice Doyle said general deterrence weighed heavily in determining the appropriate penalty.

However, he said the contempt was not as serious as other cases where jurors had been jailed for their conduct.

"I accept that [the jurors] were merely seeking to confirm their recollection of what they recalled having previously heard in media reports, rather than undertaking a more general investigation," he said.

"I also accept that neither intended to use their knowledge to sway or influence other jurors."

Justice Doyle recorded convictions against both jurors and imposed a fine of $3,000.