We describe a novel experimental technique which allows the determination of absolute oscillator strengths of Rydberg transitions with medium to high quantum numbers. Absolute photoionization cross sections measured with the saturation method are used for a calibration of the f-values. The technique and its limitations are described in detail. Results are given for the main quantum numbers n = 28 - 60 for the series Ba I (), Sr I () and for the Ba I principal series (). For the latter series a comparison with data from the literature is given.