The advantages of using superconducting windings and cryogenic temperatures in transmission electron microscopes have been recognized for some time but not fully achieved; they are: improved resolution because of higher fields and shorter focal lengths, reduced size, better vacuum, improved mechanical stability, and greater electrical stability with persistent mode of operation of lens field. At ORNL, a 500‐kV microscope is being developed with the goal of 1‐Å point‐to‐point resolution in biological specimens. All lenses will use superconducting windings operated in the persistent mode. A quadrupole‐octupole lens system will correct the primary spherical aberration of the objective. Over‐all in‐instrument magnification will be 5 ×106X. An investigation of round‐lens fields shaped primarily by currents showed that low aberrations could not be attained. Lenses using pole pieces of 1010 steel, Armco iron, and Hiperco 50 were evaluated in magnetic field tests. Typical figures are an uncorrected resolution limited by spherical aberration of 1.21‐Å in an Armco iron lens with a 7.6‐mm bore and 32‐kG field. Further work with Hiperco 50 and dysprosium pole pieces at fields above 30 kG is in progress.