For any one interested in, or working with, UV photography, one of the biggest conceptional hurdles is the notion that all colours are false by definition. Neither camera nor processing software is aware of this fundamental fact, though. Furthermore, personal preferences, the filter(s) applied, and the manner in which images are developed, all will have a huge impact on the colour palette that results. The final colours are not 'right' or 'wrong', after all they are genuinely false; they are just different.
For a good deal years now, Andrea and I have advocated a certain approach to the balancing of UV 'colours' to make the output from different cameras easier to compare in a botanical context. This scheme typically involves a filtration capable of transmitting a large portion of the 300-390(400) nm UV(A), keeping IR contamination to a minimum, and colour-balancing against a target having uniform (flat) reflectance across the recorded UV spectral band. A white Teflon/PTFE disc will do fine, but one should note that a grey disc of the same material should also record neutral. Many RAW converters can do a white balance against the [UV-]white disc, but fails to achieve a neutral balance otherwise. PhotoNinja is the reference program here as it does the UV-white balance perfectly. Andrea uses Capture NX2/NX-D, which I never managed properly myself. ACR apparently fails, as do Aftershot 2/3. It is noteworthy that the broad-band converted Panasonic GH-x can set the correct colour balance directly in camera, a feature which becomes most useful for UV video recording.
I'll dive into my archives and pull some examples of the same species Børge has shown us, just to illustrate the variation in appearance typical for UV imagery.