I have about 100 websites coded in ASP classic. Each website accepts orders and stores them in database. However, the payment of these orders must be made on another website
From the calling site you could create a guid or some other randomly generated value. Store it on the users record (set to expire in a specified time period) in the database, encrypt it and pass it over SSL to the payment site where it is decrypted and then compared to the database. If they match then the user is logged in, if it doesn't match then they are asked to log in.
Another way although I'm not sure it can be done with different domain names is using sessions. Since they are all on the same machine it might be possible but I'm not 100% sure on that one.