What browser are you using, NoScript in Firefox has been found to be one cause. You're trying to pay SE directly or via UltimatePay?

SE have posted this advice:

For Customers Receiving Error 601
If you are receiving an error 601 message when attempting to enter a new payment method or updating an old one, the error maybe caused if you are on a private network or on a company network. If possible, we recommend that you try using an outside network to register your payment method to your Square Enix Account. As repeated registration failure can lead to restrictions being placed on your account, we strongly recommend that you contact the Square Enix Support Center for guidance before attempting to register a Credit/Debit card again.
Which is very odd, hard to understand how using some type of internet connection can affect it but clearly it does.

This is another SE post in a thread on here:

http://forum.square-enix.com/ffxiv/threads/38475-Error-601-Billing-issues?p=582294&viewfull=1#post582294
Do a Google on "ffxiv error 60", you'll find many more places where this is discussed.