Microwave frequencies can harm biological function through heating tissue; in particular eyeballs have lots of water and poor ability to dissipate heat. However, very low power densities are almost certainly safe.
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Another example of non-ionizing radiation harming human tissue would be if you stick your hand in front of a cutting laser. Maybe obvious, but you asked...
[edit]
Another example of non-ionizing radiation harming human tissue would be if you stick your hand in front of a cutting laser. Maybe obvious, but you asked...