Samia Shahid, 28, from Bradford, died last month in Northern Punjab where she was visiting relatives.
Her first husband, Choudhry Shakeel, has been arrested on suspicion of her murder while her father Mohammad has been held as an accessory to murder.
Both appeared in court in Pakistan and have been remanded for four days.
The pair, who are being held while investigations continue, were shackled and had their faces covered as they appeared in court in Jhelum.
Ms Shahid's relatives had initially claimed she died of a heart attack, but her husband, Syed Mukhtar Kazam, claims she was the victim of a so-called honour killing.
A post-mortem examination has since confirmed she died as a result of being strangled, police say.
Mr Kazam, who is Ms Shahid's second husband, believes his wife was killed because her family disapproved of their marriage.
The police car which brought them to the court was surrounded by journalists. I got as close as I could to them to see if they would comment but they did not.
The media were barred from entering the courtroom and the hearing could not have lasted more than two minutes with the judge remanding them in custody for four days while the investigation into Samia Shahid's murder continues.
Police say Samia died of asphyxiation.
The father and first husband of a woman who was allegedly murdered in a so-called honour killing in Pakistan have appeared in court.