Delgado, 35, is accused of stabbing and strangling 29-year-old Robyn Renee Richardson, whose body was found in the yard of her Moler Avenue apartment on June 16, 2001.
Black claimed that Miller falsely testified before a grand jury that Delgado's blood was found inside Delgado's Chevrolet Blazer.
Black based his perjury allegation on a typed transcript of the grand jury hearing. That transcript, in turn, was taken from an audiotape used to record the proceeding. Black said he had not previously listened to the tape.
Berkeley County Prosecutor Pamela Games-Neely argued that Miller said "it is" blood in the car, not "his" - or Delgado's blood. She said whoever transcribed the hearing misheard Miller.
After a court reporter retrieved the tape, Wilkes asked reporters and other spectators to leave the courtroom because grand jury proceedings are kept secret.
Black had filed a motion demanding that the murder charge be dismissed because of the perjury allegation. However, when reporters and others were allowed back into the courtroom a couple of minutes later, Black withdrew his motion, saying the tape did not substantiate his claim.
Wilkes said the quality of the tape was not exceptional.
"It's just appalling to me that he'd do this without listening to the tape," Miller said after the hearing.
Also in court Thursday, Black asked that Delgado's trial be postponed because a piece of forensic evidence has not yet been examined by laboratory workers. Originally set to begin later this month, the trial was moved to July.
That forensic evidence was examined by employees of the West Virginia State Police's laboratory in Charleston, but was mistakenly not shipped to a separate laboratory performing tests on Delgado's behalf, both sides of the case agreed.
Police found a steak knife, with the blade bent backward, near Richardson's body. Deputy Chief Medical Examiner Dr. James Frost concluded that Richardson was stabbed 22 times. Four wounds were fatal - one to her neck and three to her chest, records show.
Delgado met Richardson on the Internet, police said.
On June 19, 2001, three days after Richardson's body was found, Delgado's girlfriend alleged to police that Delgado admitted he killed Richardson. Later that day, police arrested Delgado.
Blood was found inside his Blazer and a witness told police he saw Delgado washing the inside, but not the outside, of the Blazer the day after the slaying, according to court records.
Delgado's trial has been postponed several times, Games-Neely said.