The electrical resistivity rho and thermopower 5 of pure liquid silicon and pure liquid germanium have been carefully measured. For silicon, a new containment material was used, namely high-density graphite. This graphite has a low thermopower (6 mu V degrees C-1 at 1500 degrees C) a high resistivity (1000 mu Omega cm at 1500 degrees C), and little or no reaction with Si, making it an ideal containment material. The results for each liquid show a metallic value of resistivity, a small but positive temperature coefficient of the resistivity and a small thermopower. In particular, for liquid Si, rho = 75.2 +/- 0.6 mu Omega cm, d rho/dT = (1.7 +/- 0.9) x 10(-2) mu Omega cm degrees C-1 and 5 = -2.1 +/- 0.6 mu V degrees C-1 and, for liquid Ge, rho = 66.8 +/- 0.2 mu Omega cm, d rho/dT = (2.7 +/- 0.2) x 10(-2) mu Omega cm degrees C-1 and S = -0.3 +/- 0.5 mu V degrees C-1; all values are for the respective melting temperatures of Si and Ge. We also report a calculation of me resistivity of each liquid, using the Ziman formalism, with a recent pseudopotential and an experimental structure factor. Both our experimental and our calculated results are compared with other work.