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 , \dot { P } = 4.0 \times 10 ^ { -12 } . Under standard assumptions these parameters imply a characteristic spin-down age of only \tau _ { c } = 1.6 kyr and a surface dipole magnetic field strength of B = 4.1 \times 10 ^ { 13 } G. We have measured a stationary period-second-derivative for this pulsar , resulting in a braking index of n = 2.91 \pm 0.05 . We have also observed a glitch in the rotation of the pulsar , with fractional period change \Delta P / P = -4.4 \times 10 ^ { -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 \dot { P } = 7.4 \times 10 ^ { -13 } . These parameters imply \tau _ { c } = 85 kyr , and B = 5.5 \times 10 ^ { 13 } 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 .