A standard protocol for performance evaluation of positron emission mammography (PEM) systems has not yet been established. In this work we propose a methodology based on the design of specific phantoms for this imaging modality with component dimensions in accordance with typical breast lesion sizes together with the adaptation of current international protocols designed for clinical and preclinical positron emission tomographs (PET) systems. This methodology was used to evaluate the performance of the Flex Solo II PEM scanner in terms of spatial resolution, uniformity and contrast lesion detectability, recovery coefficients and spill-over ratios. Positron range effects were studied with 18F and 68Ga, which have very different energy spectra. Our results indicate that in-plane spatial resolution of the system is around 3.0 mm and 4.4 mm for 18F and 68Ga, respectively. Lesion detectability tests with sphere diameters between 4 and 10 mm confirmed that the PEM system can resolve all the spheres (hot or cold). Percent contrast values for 18F lie between 6%-38% and 34%-51% for hot- and cold- spheres, respectively; the corresponding intervals for 68Ga are lower, 4%-25% and 32%-44%. Regarding uniformity quantification, the system shows percentage standard deviations within 4.9%-5.7%, while the percent background variability measurements ranged between 6.7% and 10.9% for both radionuclides. Recovery coefficients measured with hot rod diameters between 1.5 and 9 mm, have values between 0.2-1.05 and 0.17-0.69 for 18F and 68Ga, respectively. Spill-over ratios have large values (0.22 in average) for both radionuclides. Our results indicate that the phantoms and the methodology developed in this work can serve as the basis for establishing an image quality protocol for the systematic evaluation of PEM systems, with a potential extension for performance evaluation of dedicated breastPET scanners.