While I have never experienced this pain myself, I was the postpartum and baby nurse for a mom who had a baby with Trisomy 13, in which the infants don't live long after birth. This was almost 15 years ago and things have changed some, but I can share with you what we did for her, things that are do-able in any hospital with a high-risk unit:
We let her keep the baby with her as much as possible. When she was resting, we put the baby in a private area of the nursery so that family members could come in and take their time to see the baby and say good-bye. Her postpartum room was in an area of the unit as far away from moms with crying babies and joyous families as possible in order to spare her the pain of hearing those other babies cry when her own little one wasn't long for this earth. She held him, dressed him, bathed him, and held him some more. We got pictures for her and with her. We called in the priest (the family was Catholic) so the baby could be baptized. We encouraged her to talk, to share her pain, to cry...it's important to cry and grieve for the life you've carried inside you for all this time. It's okay to hurt and be in pain.
Most hospitals now have a special place for babies that pass on either before birth, during birth, or shortly after. I worked at one here in our area right before I got sick and we had an open-room policy where any time Mom and Dad wanted to see the baby while Mom was still a patient, all she had to do was let us know and we would go and get the baby for her so she could hold him/her, touch him/her, or just spend time with the baby in the room. When we would go get the baby, we would put clothing and a blanket on him or her. These items of clothing were given to the parents upon discharge so they had a point of contact for themselves and the baby. If you have an outfit you would like the baby to wear so you can take it home with you for a memory book or box, try to remember to bring it with you. This can be accommodated. You can have a locket of the hair.
Remember more than anything that this is a loss, and that you will grieve, and that it is a perfectly normal thing for you to cry for what seems like no reason at all for weeks or even months. Moms and Dads put so much into growing a baby; it's a tremendous loss and a shock to your system. This isn't how it's supposed to be. You're supposed to have a baby in your arms, holding them and watching them grow, and you've been denied that opportunity. Please take advantage of support groups, whether online or in your area. It helps you remember that you have peers who are also suffering and that helps validate what you are feeling.
Encourage family members to hold the baby, touch him or her, and express how they're feeling. They, too, were anticipating a healthy baby. Remember that you have people to lean on. Use that when you're exhausted and need a break or when you need a hug.
You are in my prayers, as is your family. This should be a joyous time, not a time of grieving. It's not fair, and it's okay to think that. Know also that with time the pain will lessen, though it will never go away. Gather what memories you can, treasure them, and draw strength from each other.