Note the Nazguls' actions after Frodo puts on the ring in the dell near Weathertop.
Quote:
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Immediately, though everything else remained as before, dim and dark, the shapes became terribly clear. He was able to see beneath their black wrappings. There were five tall figures: two standing on the lip of the dell, three advancing. In their white faces burned keen and merciless eyes; under their mantles were long grey robes; upon their grey hairs were helms of silver; in their haggard hands were swords of steel. Their eyes fell on him and pierced him, as they rushed towards him. Desperate, he drew his own sword, and it seemed to him that it flickered red, as if it was a firebrand. Two of the figures halted. The third was taller than the others: his hair was long and gleaming and on his helm was a crown. In one hand he held a long sword, and in the other a knife; both the knife and the hand that held it glowed with a pale light. He sprang forward and bore down on Frodo.
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I think Tolkien is insinuating the 3rd was the Witch King, but you can see that two of the nazgul halted when Frodo drew his sword. Whether you can call this 'cowardice' or not I'm not sure, but they don't seem too inclined to attack a lowly hobbit (albeit wearing the one ring which may possibly have given him extra 'power')......