How would you comfort someone that has ptsd after a nightmare?

Comfort: It depends on the person, but in general warm support and reorienting (reminding) them of the safety in the immediate physical environment they are in and present circumstances. Professional counselling from a clinical psychologist or psychiatrist might also be helpful for other suggestions.

Stay calm.: If you over-react, so will they. In actuality, you have it reversed. The nightmare does not cause ptsd, although people with ptsd frequently have nightmares. Just try to make sure they are fully oriented, with enough light to see you and everything in the room. If necessary, tell them softly where they are, who you are, and reassure them that they are safe and it was just a bad dream.

Nightmares: Nightmares are a common symptom in PTSD, but the traumatic experience occurred first, then the nightmare. Don't wake them up unless they start to get out of bed and walk, but even then be very careful. I teach No More Nightmares-How to Use Planned Dream Intervention to End Nightmares and people with nightmares and flash backs will rapidly stop having both. Expert trauma tx, I recommend EMDR as bes