Not "almost no resistance" Jake, None at all or they are not superconductors.
One of the major problems with high temperature superconductors is magnetic fields.
Most known superconductors are superdiamagnetic meaning that they exclude magnetic fields. However the superconductiing effect is lost if the field becomes strong enough to penetrate the material. Since all currents produce magnetic fields proportional to the current it is a substantial problem.
However a new class of "high temperature" superconductors was discoved in 2008. These are iron pnictide (silent p) materials. While the high temperature is a chilly 4K the material is not superparamagnetic. Moreover, unlike copper oxide alloys it is not a ceramic.
Although this temperature still requires liquid helium refrigerant, It must be remembered that the situation was the same when copper alloys were first discovered to be superconductors. There were susequently developed to reach transition temperatures of 138K allowing for liquid nitrogen coolant to be used.
Another important aspect of this new material is that it provides a basis for comparison or two different materials which may elucidate the physics of the phenomonon which is still not well understood. Once comprehended it may eventually be possible to design room temperature superconductors.
http://physics.aps.org/articles/v1/21
http://www.superconductors.org/