Some FDs hit harder than others, and there may not be any rhyme or reason as to why. It's normal, and allow yourself to feel whatever you feel. I've found that families appreciate a few tears shed in their presence, it makes you human and shows you care.
However, if you have to 'lose it', it's probably a good idea to do it elsewhere, so the family that needs comforting doesn't end up feeling they need to comfort you. (I've had to lose it many times; it means you are a normal human, it just needs to be a proper outlet.)
Some families don't want to look at their babies after delivery. It's not up to you and me to decide for them what they need. Sometimes people don't want to look because they are afraid the baby is grossly deformed, other times it's because they think it will be hard to see a perfect baby and wonder forever what went wrong. I tell people that no one will force them to do anything, but that sometimes having something concrete to grieve will help them grieve more effectively, and if they want a description of the baby, I give it to them. In any case, we make the memory box with pics, a lock of hair if possible, hand/footprints, and whatever other mementos we can give them, and tell them it's all there whenever they are ready to see it.
Ask, ask, ask if they want a chaplain or their own religious leader/clergy to visit, whatever their faith. They may not, but some people take great comfort in this.
Please remember the baby's father, if he is present/involved. I think we (rightly) spend a lot of time meeting Mom's needs, but fathers grieve too. Their needs are different, and their grief manifests differently, but they do hurt and grieve, and I think it's easy to forget. If I can get a moment, I pull the father aside and make sure he is doing okay and see if he has any questions he wants to ask but is afraid to ask in front of mom. It makes a huge difference. I haven't always done that, but I had one FD that changed the way I practice and ever since, I have tried my best to include fathers in the process.
Hope this helps. It don't ever get easy.