We (20-person privately held company) have a registered trademark that
we are not actively using but might want to use in the future. 
Another company (110-person privately held company) wants to use it
but has been rejected by the PTO because we're in similar industries. 
Can we contractually do a deal where we agree to give up our mark for
a fee?  What is a *fair* fee or fee range?

Trademarks are frequently sold. The fee depends entirely upon the
desireability of the trademark. If a buyer wants it very badly, it's
worth a lot of money. If not, it isn't. For example, Rolls Royce sold
the trademark term "Rolls Royce" to BMW for $65 million. A friend of
mine who runs a small business recently sold the rights to a
seldom-used trademark that he owns. He was only able to get $200 for
it.

Howdy dansker47-ga,

Have the other company make you an offer.  Their perceived value of the
trademark might very well be more than yours.

Looking Forward, denco-ga - Google Answers Reseacher