Upper critical magnetic fieldsHc2(T) have been measured resistively for the high‐temperature (Tc≳90 K) superconductors TmBa2Cu3O9−&dgr;and YBa2Cu3O9−&dgr;in applied magnetic fieldsHup to 9 T. IfHat the resistive midpoint is defined asHc2, then the upper critical field slopes (dHc2/dT)Tcat the superconducting transition temperaturesTcare respectively −2.8 and −1.1 T/K. The Tm‐specimen initial slope is apparently the highest yet reported for 90 K superconductors. Extrapolations from this slope, based on standard, three‐dimensional, dirty‐limit Werthamer, Helfand, Hohenberg, and Maki theory, yield (1) zero‐temperature upper critical fieldsHc2(T=0)=99–175 T, where the range is determined by the degree of paramagnetic limitation; (2)Hc2(T=77 K)≊36 T, the upper critical field at the boiling point of liquid nitrogen.