You know what, the fact that you use a Super Cap is not really an issue because as others stated it's going to pull the current it needs...
But, I use a 14.5v car battery charger which is connected to an SLA battery 7a/h , Now i have a voltage line going through a fuse into a Step Down voltage Regulator which can deliver 3 amps at 12v's quite nicely, it's perfect for Arduino boards..
But, be careful if you use the super cap to power other components on the breadboard, last thing you want to do is short out a super cap while wiring it up on the breadboard, 3amps is scary enough for a short, what about a super cap? discharge time faster than you can say "ouch i burnt myself"