Frequency-dependent molar electrical conductivities for aqueous solutions of boric acid with small additions of sodium hydroxide or potassium hydroxide have been measured from 298 to 573 K at 12 MPa to an accuracy of +/- 3%, using a unique high-precision flow-through AC conductance instrument. The measurements were made to yield accurate polyborate equilibrium formation constants and limiting conductivities under the primary coolant conditions of pressurized water nuclear reactors (PWRs). Complementary measurements from T = 283 K to T = 313 K at p = 0.1 MPa were completed using a commercial conductivity probe to extend the data to lower temperatures. Up to 423 K, measurements were performed under conditions where the triborate ion B3O3(OH)(4)(-) is the major anionic species in solution. At temperatures above 473 K, the conditions favored the formation of a different anionic species, which was assigned to be the diborate ion B-2(OH)(7)(-). The analysis of the concentration dependence of the molar conductivity data using the TBBK equation yielded limiting conductivities, lambda(0), and formation constants, K-31,m(b) and K-21,m(b) for triborate and diborate from 283 to 473 K, and from 473 to 573 K, respectively. These results are consistent with the only other experimental study that has reported equilibrium constants for aqueous polyborates above 373 K (Mesmer et al. Inorg. Chem. 1972, 11, 537). The limiting conductivities are the first to be reported in the literature.