We determine the band alignment at the CaF2/Si(111) interface through various advanced electronic-structure methods. This interface is experimentally well-studied and serves as an ideal test case to examine the accuracy of theoretical schemes. We use both global and range-separated hybrid functionals as well as GW calculations including self-consistency and vertex corrections. Our calculation procedure accounts for residual strain resulting from the small mismatch in the lateral lattice constants at the interface to minimize the systematic error in the comparison with experiment. Both the hybrid-functional and the GW schemes give band alignments in overall good agreement with the experimental characterization. However, the considered methods yield sizable variations in the calculated band offsets, which do not originate from incorrect evaluations of the band gaps but rather from different inherent relative positions of the band edges. The comparison with experiment reveals that the global hybrid functional and the quasiparticle self-consistent GW with vertex corrections give the most accurate description of the band alignment. We then determine the variation of the band offsets as a function of the amount of excess fluorine at the interface and attribute the experimental spread in the measured offsets to uncontrolled fluorine contamination.