It has a special kiosk as seats ar e often reserved. But I can find no information as to whether the cards are sold per machine or agent. Nor can I confirm if it is pre-paid or bills directly to a CC. I know there is a VISA that links and works as a IC card as a supplement to the EX-IC, however JR-C's website has only a small PDF on the use of the card which is not even accessible from the main navigation anymore and it does not denote in the English page on acquiring the card. http://english.jr-central.co.jp/about/_pdf/about_express_reservation_service.pdf
From the brief Japanese description I read, it looks like you have to use it together with a prepaid IC card like a Suica card. Presumably the Suica card handles payment and the EX-IC identifies your reservation. I could be wrong though.
(If reservations can be done by IC card, what do you show the conductor when he comes to check your ticket?)
