"Mr Stanford was found to have an irregular electrocardiogram and an extremely high pulse rate," US district judge David Hittner said at a hearing.
Dick DeGuerin, Stanford's lawyer, said his client has a history of high blood pressure and has faced difficulties in getting medication at the Texas jail where he is being held pending trial.
Davis signed a plea bargain with US government prosecutors and has been co-operating with them for the last six months.
He will forfeit $1bn under the agreement, which will allow the government to seize any assets.
Paul Pelletier, the principal deputy chief with the US department of justice in Washington, said that Stanford and Davis "duped" investors out of billions of dollars by falsifying documents and paying-off regulators and accountants in Antigua.
"I did wrong. I'm sorry," Davis, who was accompanied by his wife, said after the hearing.
"I apologise. I take responsibility for my actions."
He admitted carrying out two acts of fraud and conspiring to obstruct an investigation by the Securities and Exchange Commission.
Davis, who faces a maximum of 30 years in prison on conspiracy, fraud and obstruction charges, has been free on $500,000 bail since he first appeared in court on July, when he pleaded not guilty.
Stanford, who has pleaded not guilty to the charges, implied in media interviews before his arrest that Davis was responsible for the fraud, a claim dismissed by David Finn, Davis' lawyer.
Finn said the government is aiming to unearth assets while investigating Leroy King, the Antiguan regulator, who is accused of taking bribes from Stanford.