Remus is obviously there while she waits. He'd only step in her room when it wasn't crowded so she wasn't overwhelmed. He'd even tell her to let him know if his visits were too much.
When the baby was actually born, he'd have very manly, teary eyes as he held her for the first time. He'd snog Tonks so hard outside the hospital because seeing that little girl shows him they made a real difference in the world even if they weren't around to witness Teddy become the man who makes such beautiful babies.
It is a very bittersweet, emotionally draining, and fulfilling day. He loves you all.