We discuss circular scanning Fluorescence Correlation Spectroscopy (sFCS) as a simple extension of standard FCS for accurate, robust and fast diffusion measurements on membranes. The implementation is based on a straightforward conversion of a conventional FCS instrument to a sFCS device by mounting a mirror onto a two-axis piezo scanner. The measurement volume is scanned in a circle with sub-micron radius, allowing the determination of diffusion coefficients and concentrations without any a priori knowledge of the size of the detection volume. This is highly important in measurements on two-dimensional surfaces, where the volume size, and therefore the quantitative outcome of the experiment, is determined by the relative position of the surface and the objective focus, a parameter difficult to control in practice. The technique is applied to diffusion measurements on model membrane systems: supported lipid bilayers and giant unilamellar vesicles. We show that the method is insensitive to membrane positioning and to disturbing processes on faster or slower time scales than diffusion, and yields accurate results even for fluctuating or drifting membranes. Its robustness, short measurement times, and small size of the probed area makes this technique particularly attractive for analyzing the properties of membranes and molecules diffusing and interacting within them.