Eddy current brakes (wiki) --- a.k.a. magnetic brakes --- get quite some attention from train engineers. They are used on Shinkansens, roller coasters, and even (as far as I know) metro trains on Lane C in Prague. They basically consist of a magnet and a rotating disk, where these two never touch. The kinetic energy is converted to heat, as in conventional brakes. While Shinkansens give them up, from what I view it is in favour of recuperating brakes and whence it is irrelevant with respect to aviation.
I wonder whether anyone considered their use in aviation. To me it seems that it could be a good option.