We present a tabletop setup for extreme ultraviolet (EUV) reflection spectroscopy in the spectral range from 40 to 100 eV by using high-harmonic radiation. The simultaneous measurement of reference and sample spectra with high energy resolution provides extremely precise and robust absolute reflectivity measurements, even when operating with unstable and spectrally fluctuating EUV sources. We demonstrate the performance of the setup by reflective near-edge x-ray absorption fine structure (NEXAFS) measurements of the aluminium L2/3 absorption edge in U-Al2O3 and compare the results to measurements using synchrotron radiation. We show that the accuracy and stability of the self-referenced reflectivity measurements is almost one order of magnitude better as compared to the conventional method of independently recording the spectra of the source and the reflection at the sample.