His-tagged molecules can be attached to lipid bilayers via certain anchor lipids, a method that has been widely used for the biofunctionalization of membranes and vesicles. To observe the membrane-bound molecules, it is useful to consider His-tagged molecules that are fluorescent as well. Here, we study two such molecules, green fluorescence protein (GFP) and green-fluorescent fluorescein isothiocyanate (FITC), both of which are tagged with a chain of six histidines (6H) that bind to the anchor lipids within the bilayers. The His-tag 6H is much smaller than the GFP molecule but somewhat larger than the FITC dye. The lipid bilayers form giant unilamellar vesicles (GUVs), the behavior of which can be directly observed in the optical microscope. We apply and compare three well-established preparation methods for GUVs: electroformation on platinum wire, polyvinyl alcohol (PVA) hydrogel swelling, and electroformation on indium tin oxide (ITO) glass. Microfluidics is used to expose the GUVs to a constant fluorophore concentration in the exterior solution. The brightness of membrane-bound 6H-GFP exceeds the brightness of membrane-bound 6H-FITC, in contrast to the quantum yields of the two fluorophores in solution. In fact, 6H-FITC is observed to be strongly quenched by the anchor lipids which bind the fluorophores via Ni2+ ions. For both 6H-GFP and 6H-FITC, the membrane fluorescence is measured as a function of the fluorophores' molar concentration. The theoretical analysis of these data leads to the equilibrium dissociation constants Kd = 37.5 nM for 6H-GFP and Kd = 18.5 nM for 6H-FITC. We also observe a strong pH-dependence of the membrane fluorescence.