Do not be terrified, do not be discouraged, for the LORD your God will be with you wherever you may go. Joshua 1:9
I would all of a sudden become convinced that John was going to die, and I would have to give birth and raise Emma alone, or I would be overcome by the possibility that Emma could be born with severe defects. John would wake up and pray with me, over me and for me. I memorized and meditated on scripture about trusting God, about not fearing. And it helped.
God has not given us a spirit of fear, but of power, love, and a sound mind.
After Emma was born the fear subsided. There was (still is sometimes) definitely the first time parent nervousness of checking and double checking her breathing while she slept, wondering if she really is okay, if she is growing normally, if I am a "good" mother. But overall I have been able to turn those fears over to God and He has given/is giving me the grace to trust Him.
God is able to make all grace abound to you ... II Corinthians 9:8