In this paper, a data efficient machine learning (ML)-based framework for the prediction of key-features of the power delivery network (PDN) impedance is proposed. Gaussian Process Regression (GPR) is implemented within transfer and active learning loops to explore the potential with regard to data efficiency and accuracy. For a 4 layered printed circuit board (PCB), a prediction accuracy with a normalized root mean squared error (RMSE) of 3 % is achieved for some features including the resonance frequency of the board. The use of transfer learning results in a higher data efficiency and faster convergence. It is shown that reusing data from closer problems reduces the amount of new samples that need to be generated. The higher data efficiency makes ML tools a more attractive approach to speed up PDN design by replacing the expensive electromagnetic (EM) simulations of PCBs.