In this paper we apply two methodologies to the measurement of efficiency in Portuguese Universities. These are a stochastic frontier parametric method and a non-parametric DEA method. We produce results from both methods in terms of efficiency estimates for each university over the period 2003 to 2005. We also produce, in both methods, unitary cost estimates of teaching students (undergraduates, master, and doctoral students) and of producing research outputs. Results from both methods can be said to be coincident to a certain extent, especially in what concerns the identification of worst performers. The productivity change of Portuguese universities in the period 2003-2005 was also explored using Malmquist indices.