I just returned from Copenhagen, Denmark. To purchase train tickets from the airport one can use either cash or a chip&PIN card. Neither the automatic ticket machines nor the manned ticket booth accept a mag-stripe-only card.
I did try my Amex and a bogus PIN on the automatic machine- no go. The ticket booth has two signs (a small stick-on and a larger paper printed) stating that only a card with PIN would be accepted.
My only recourse was the ATM down the hall which happily dispensed cash to my BoA debit card using my regular PIN.