I've actually got a circle cutting jig for the scroll saw, made by Diamond. You bolt a swiveling pin through a hole drilled into the plywood table and slide a trammel bar through the top of the pin. Then you extend another pin through the end of the trammel bar and hold the wood in place at the required radius from the blade. After that, it's just a matter of spinning the wood and the blade will do the work, rather like your bandsaw jig, Chas.
That's the theory.
However, scrollsaw blades don't cut straight because they have a bias, usually to the right. So I find that in practice the blade will try to wander off course, leaving you with a misshapen piece.
If you have no choice but to cut a circle with a scroll saw, the best technique is the one that Toni outlined above. It gives you a chance to make slight adjustments as you cut so that you don't wander off-line. Indeed, I cut a couple of discs freehand in this way the other day with the table angled so that the discs were tapered. They came out rather well and made acceptable airtight bungs at either end of my new dust extraction pipes.
Nevertheless, I still advocate a router as generally being the best tool for this task.
Gill