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Organs cryopreserved by vitrification benefit from fast warming to avoid growth and recrystallization of ice that may nucleate during cooling and during warming. Rapid warming is especially important for tissue that doesn't absorb the full concentration of perfused cryoprotectants. Nanowarming uses an oscillating magnetic field to heat magnetic nanoparticles introduced into blood vessels during cryoprotectant perfusion. Dielectric warming uses an oscillating electric field to directly heat water and cryoprotectant molecules everywhere inside an organ. The efficiency of dielectric warming peaks at a particular solution viscosity and temperature that depends on the field oscillation frequency. Below that temperature, field uniformity is very important for uniform warming. An 800 W 55 MHz dielectric warming system was constructed that reached peak warming efficiency at -60 °C instead of -70 °C previously observed at 27 MHz when using the M22 vitrification solution. The shape of capacitor plates that formed the electric field for organ warming was optimized by computer simulation. Computer simulation also provided insights into the effects of organ container shape on internal field uniformity, confirming the theoretical prediction that ellipsoidal shapes are optimum. Dielectric materials surrounding the organ container during warming were used with beneficial effect. In physical experiments with constant field warming at 55 MHz, warming rates peaked near 200 °C/min for ∼15 g rabbit kidneys in 45 mL total volume, and near 700 °C/min for ∼5 g porcine ovaries in 15 mL total volume. Of three rabbit kidneys vitrified, dielectrically warmed under slightly varying conditions, and then transplanted, one survived long-term with return to normal clinical function (serum creatinine <2 mg/dL) in the recipient animal still living 17 months later. The mass of the kidney was 13.9 g, by an order of magnitude the largest vitrified vital organ successfully returned to clinically normal function to date.