"I wonder if somewhere out there, a star orbits a planet. Would such a thing be possible, a Superjovian circled by a star or two?"

Not really. It depends how you define things. A Superjovian with 10 times it's mass is a Star. Without the fusion reaction of a star, the gravity from it's mass would cause it to keep on collapsing until you a neutron star or dwarf star. Now you could have cooled Dwarf star and call that a planet or fragment of neutron star or cooled dwarf star, but gravitational forces would crush you.
You could make an artifical planet- a dyson sphere:
"What is a Dyson Sphere?
The Dyson sphere (or Dyson shell) was originally proposed in 1959 by the astronomer Freeman Dyson in "Search for Artificial Stellar Sources of Infrared Radiation" in Science as a way for an advanced civilisation to utilise all of the energy radiated by their sun. It is an artificial sphere the size of an planetary orbit. The sphere would consist of a shell of solar collectors or habitats around the star, so that all (or at least a significant amount) energy will hit a receiving surface where it can be used. This would create a huge living space and gather enormous amounts of energy.
A Dyson sphere in the solar system, with a radius of one AU would have a surface area of at least 2.72e17 km^2, around 600 million times the surface area of the Earth. The sun has a energy output of around 4e26 W, of which most would be available to do useful work.

The original proposal simply assumed there would be enough solar collectors around the star to absorb the starlight, not that they would form a continuous shell. Rather, the shell would consist of independently orbiting structures, around a million kilometres thick and containing more than 1e5 objects. But various science fiction authors seem to have misinterpreted the concept to mean a solid shell enclosing the star, usually having an inhabitable surface on the inside, and this idea was so compelling that it has been the main use of the term in science fiction. The earliest appearance of this version seems to be Robert Silverberg's novel Across a Billion Years.

A third kind of shell would be very thin and non-rotating, held up by the radiation pressure of the sun. It would consist of statites (see below, in the section about stability). Essentially it is a "dyson bubble", where reflecting sails reflect light onto collectors for use in external habitats. Its mass would be very smalll, on the order of a small moon or large asteroid. "
http://www.nada.kth.se/~asa/dysonFAQ.html#WHAT

I'm thinking the latter "dyson bubble". Of course the orbiting star wouldn't really be orbiting the planet [dyson bubble] but the star in it's interior. Of course having a star orbit this would cause some problems in it's graviational stability- though perhaps you could design it so it interacts this instablity so it's stable. I don't know how exactly, but suppose you work with it's L-points??
Let's take our solar system, say Jupiter was 20 times it's mass- making it a star. Since Jupiter is currently about 1% of the mass of the Sun, that would make it a sun which 20% of the Sun's mass.
Hmm, don't know what that orbit would look like. The earth moon is 80 to 1 and Pluto Charon is about 65 to 1, so this 5 to 1 is definitely going to tug on the Sun, but suspect just going to make wobble a lot more.
And not orbit around. Even if Jupiter was same mass of Sun, they will orbit around a point halfway between them. You could put a planet at that midpoint and it could be a stable orbit- and it could sort of look like two Suns are orbiting, but they aren't really orbiting this planet anymore than the Sun is orbiting Earth.

So, back to first answer: not really.