Marcelo, I think is possible to obtain microhardness (vickers) values, but the quality of the results will depend of the setup of the microhardness tests, you need to be sure about the contact between the surface and ribbons, actually I´m not sure about "20 mm thick" which is the Length, wide, and thickness of these ribbons? because if the thickness is small, could be better nanoindentation.
I suppose you are asking about 20 micron thick ribbons. Microhardness testing is possible with say 100 g or less making sure the surface is right angles to the indenter. Other possibility is nano indentation testing.
You need a certain depth of material to provide full plastic constraint for the indent. The depth of the indent depends upon load and hardness of the material under test. If you know a ballpark figure for the ribbon's hardness you can compute the required sample thickness for a valid result. The procedure IIRC is given in the various international hardness testing standards. However, that being said (even when indent is fully plastically constrained, i.e. sample is thick enough for a valid test at the set indent load) there are a few odd things which happen as you reduce the indent load, i.e. some materials appear to get harder, and some appear to get softer. I can not lay my hands on the references involved, but I have seen this reported in the literature. I have not kept up with the literature on nano-indentation, but an expert in that field is probably the person to talk to for testing ultra thin strip.
Back in the 1980s we did melt spinning and planar flow casting, PFC, of metallic glass alloys, and we tried standard microhardness testing . Results were ok, but not fantastic, we had a practical limitation on accuracy simply due to problem in defining the edges of the indents, even when we PFC which gave a bit better strip profile/surface quality.
You might use these techniques (and/or Knoop) and then measure the indents with a calibrated SEM method, that is one way to get round the limitations of the optical microscope normally used to measure the indents on the testing machine.