I've not used Swish before and like you said I can't access the login page either. However, I never got any account details so do you know how you would login?
Edit: Managed to get on the page and create an account after some f5 hammering. Turns out all you need to do is create an account with the same email you used in the order and it will display the order status.
We wanted to make checkout easy, but maybe went a little too far. I'll add some more language to the confirmation email explaining what's going on. Thanks for posting the solution.
Edit: Managed to get on the page and create an account after some f5 hammering. Turns out all you need to do is create an account with the same email you used in the order and it will display the order status.