Last time I used my miles on Delta, about a year or so ago, I was charged $10 a ticket, I guess they went up quite a bit since then.
A month ago I used my miles for Delta, through Vista Credit Union and was charged nothing. I asked the man on the phone about this and he said that it's a service they provide, so no charge.
I also used award tickets on Jet Blue recently, if you do it online, there is no charge and if you call there is a charge of $10. a person.