Dudley Group NHS Trust pleaded guilty to failings "posing a significant risk of avoidable harm" in July relating to the deaths of mother-of-six Natalie Billingham, from Tipton, and teenager Kaysie-Jane Robinson, from Netherton.
A short hearing was held at Dudley Magistrates Court on Friday, where sentencing was fixed for November 18. The court was told the hearing is likely to last two days.
The proceedings followed an investigation by the Care Quality Commission (CQC) into the care provided by the trust before their deaths.
The charges admitted by the trust stated that it had failed to provide treatment in a safe way at Russells Hall Hospital, resulting in harm, in February and March 2018.
The Dudley Group's lawyer, Paul Spencer, previously said the organisation’s guilty plea in respect of Ms Billingham, 33, was being entered on the basis that it did not accept its failings led to her death.
But Mr Spencer added that the trust did accept that the “poor care and treatment” of 14-year-old Kaysie-Jane had caused her death. Both patients had been treated for sepsis.
District Judge Graham Wilkinson said the sooner the trust is sentenced the "better for families trapped in this cycle".