I figure that Mie scattering is best for finding the scattering when the wavelengths are between 1/10th to 10x the particle diameter. However, is there an upper limit to this? If I send 2.8cm microwaves into a 10cm sphere, will it scatter according to Mie Scattering?
To add to John Rennie's answer: the Mie solution is valid for any wavelength / particle diameter ratio. However, beyond the range indicated in the question, much simpler theories may give a decent accuracy (it also strongly depends on the electric properties of the sphere though), so using the Mie solution may be an overkill.