As hard X-ray microprobes use X-rays to excite X-ray fluorescence in the specimen, there is very little bremsstrahlungsbackground, therefore, the specimen support need not be as thin as often is required for electron microscopy. Nevertheless, usually thinner is better than thicker.
One 'typical' specimen mount we use are electron microscopy grids, usually gold with formvar/carbon coating. The london finder type grids are very useful, as they have letters on the grid that are easily visible in both optical light microscopy and X-ray microscopy, thereby greatly facilitating finding the same cells in the two instruments. There are plenty of sources for EM grids 'out there', one source, e.g., is Electron Microscopy Sciences. Usually the grid material is chosen so as to minimise intereference with the elements one is interested in analysing (obviously, if one is interested in trace amounts of Cu in cells, analysing cells on a Cu grid is maybe not a good idea). Even when one is not interested in a specific element (like, e.g., Ni) it is often a good idea to choose a grid made of an element that has absorption edges that are far away (ideally above) from the incident energy. Otherwise, X-rays scattered of the sample will hit the grid structure, cause fluorescence of the metal grid, and will lead to a very large peak for that element, reducing the sensitivity for neighboring elements, and increasing the total countrate on the fluorescence detector, with consequently decreased detector performance. The choice of gold as a grid material is only advantageous (from an X-ray analysis perspective) as long as the excitation energy is below the gold L lines. Also, the gold M lines are situated between P and S, which decreases the sensitivty for this two elements as one gets close to grid bars.
A different kind of specimen support that we find quite useful are Si3N4 windows. Personally, I 'like' the ones with 5x5 mm window frames, and 2x2 mm window area. A good standard thickness of the window is 200nm (the frame is typically 200 microns), thinner ones show less background, abut are much more fragile. In particular with cells that attach strongly to the substrate (like fibroblasts), these can be too thin, the 1 micron thick ones work better. Si3N4 windows have the disadvantage that they have a strong Si background, and that there is no direct reference grid on the substrate. The latter can be worked around by using the corners as fiducial markers, and then useing precise stages to determine cell locations in the light microscope and convert their positions to X-ray microprobe coordinates. One source of these windows is Silson.
Please note: I have no affiliation with the companies listed above. I have used their products in the past, and l listed them as an example of suppliers. By no means is that any judgement as to the quality of their products.