Oxygen diffusion is treated in a dense electronically conducting cobaltate pellet blocked ionically on one surface, electronically on the other, and sealed on its cylindrical periphery. A procedure is developed for extracting the chemical diffusion and surface exchange coefficients for oxygen by use of the asymptotic equations derived for the current response to a potential step at short and long times. It is shown that, while the formation of interfacial phases by reaction between the sample and the electrolyte may affect the surface exchange coefficient, the chemical diffusion coefficient data determined by the present approach are independent of such interfacial phenomena. The consistency of data obtained from several specimens with varying thickness and manner of interfacing with the electrolyte validates the diffusion model and the method used for data analysis. An oxygen permeation cell is also developed in this work as a modification of the diffusion cell. The new cell allows monitoring of the permeation rate by electrochemical means. The steady-state permeation data obtained by the permeation cell are consistent with the chemical-diffusion and surface-exchange coefficients measured by the blocked diffusion cell as long as the assumptions of the related theoretical models are satisfied. This is a further validation of the diffusion model and the related methodology developed here for obtaining the necessary data for characterizing oxygen exchange and transport in such materials.