NPR carried a segment from WBUR Boston on a woman who discovered late in pregnancy she had a deformed fetus that could die at any time. Listen to her story here - WBUR Here and NOW. Segment is on the page.

The woman said she went to the late Dr. Tiller (recently murdered and called 'Baby Killer' by Bill O'Reilly) when her own doctor told her to wait until the baby dies in her womb. Alternatively, if she goes into contractions, she could deliver it and she could hold it until it dies. She said she could not stand either of these choices and a nurse mentioned that a Dr. Tiller in Kansas might help her in her situation.

 The woman lived in Virginia and traveled to Kansas to get a late term abortion. On the interview linked above, she said she felt he had saved her life.  The woman was thankful for his services. She believed all of his late abortions were on severely damaged fetuses like hers.

In cases like this where God is a baby killer, PubMed reports on Catholic Hospitals:

Catholic-owned hospital ethics committees denied approval of uterine evacuation while fetal heart tones were still present, forcing physicians to delay care or transport miscarrying patients to non-Catholic-owned facilities. Some physicians intentionally violated protocol because they felt patient safety was compromised. Although Catholic doctrine officially deems abortion permissible to preserve the life of the woman, Catholic-owned hospital ethics committees differ in their interpretation of how much health risk constitutes a threat to a woman's life.

An anecdotal report of miscarriage handling at Catholic hospitals:

After one of my wife's miscarriages, a neighbor and friend who is about 10-15 years older than us told us the story of her own miscarriage. She hadn't realized that her OB only had admitting rights at the local Catholic hospital. When the pregnancy (pardon my euphemisms- they're emotional baggage from my own experience) became clearly non-viable, our friend's OB *could not give her a D&C* to cut short the physical and emotional pain of the miscarriage and she was forced to go through it "naturally." As I recall, she was partway through the 2nd trimester- so this was very painful physically and emotionally.

A Catholic Hospital may not be the best place to go it you are experiencing a miscarriage, but a Catholic priest can advise you on how to handle the baby that God killed:

Question
I had a miscarriage on my 5th week of pregnancy.  I was able to save the tissue that contains the very tiny embryo.  What should I do to give my baby a proper burial?  Is it necessary to hold a vigil, funeral service, and Mass for my unborn baby?  I plan to bury my baby in a large decorative pot because I live in an apartment (I don't have a garden, only a balcony).  Then I will plant a nice rose bush in this pot as a memorial for my baby.  Is this a good idea?  Please give me advice.  I want to do what is right according to Roman Catholic Teachings.  Please help.  Thank you.  

Answer
Hazell,

I am sorry for your loss. Call any funeral home and they will give you a small casket. Most cemeteries have a place called "Babyland" where the baby can be buried for free. A priest can be called and will say prayers and blessings.
Fr. Meinen