We report the discovery of two young isolated radio pulsars with very high inferred magnetic fields. PSR J1119-6127 has period P = 0.407 s, and the largest period derivative known among radio pulsars, Pdot = 4.0e-12. Under standard assumptions these parameters imply a characteristic spin-down age of only tau = 1.6 kyr and a surface dipole magnetic field strength of B = 4.1e13 G. We have measured a stationary period-second-derivative for this pulsar, resulting in a braking index of n = 2.91+-0.05. We have also observed a glitch in the rotation of the pulsar, with fractional period change Delta_P/P = -4.4e-9. Archival radio imaging data suggest the presence of a previously uncataloged supernova remnant centered on the pulsar. The second pulsar, PSR J1814-1744, has P = 3.975 s and Pdot = 7.4e-13. These parameters imply tau = 85 kyr, and B = 5.5e13 G, the largest of any known radio pulsar. Both PSR J1119-6127 and PSR J1814-1744 show apparently normal radio emission in a regime of magnetic field strength where some models predict that no emission should occur. Also, PSR J1814-1744 has spin parameters similar to the anomalous X-ray pulsar (AXP) 1E 2259+586, but shows no discernible X-ray emission. If AXPs are isolated, high magnetic field neutron stars (``magnetars), these results suggest that their unusual attributes are unlikely to be merely a consequence of their very high inferred magnetic fields.
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