The "Fair" Sex in LotR

I think that Tolkien had a profound respect for women.

Take Galadriel. As far as I know, she is the oldest living Elf in Middle Earth at the time of LotR. As such, her wisdom is beyond all others. Also, she is one of the three ring-bearers of the elves. There were certainly good reasons for her being chosen as a ring-bearer out of thousands of elves.

Take Eowyn. Throughout the books (especially RotK) the Nazgul wreak incredible fear on the greatest warriors of Minas Tirith. It was Eowyn that stood in the midst of the Witch King and drove her sword through his head.

I think those two examples are definitely enough, but even beyond that, when characters discuss the women (especially Galadriel and Arwen) it is obvious they have a very high regard for them. Gimli, for example is ready to come to blows with Eomer when Eomer insults Galadriel, the lady of the Wood.