Jamieson, Fausset and Brown on Esther 5:2

2. the king held out to Esther the golden sceptre that was in his hand--This golden scepter receives an interesting illustration from the sculptured monuments of Persia and Assyria. In the bas-reliefs of Persepolis, copied by Sir Robert Ker Porter, we see King Darius enthroned in the midst of his court, and walking abroad in equal state; in either case he carries in his right hand a slender rod or wand, about equal in length to his own height, ornamented with a small knob at the summit. In the Assyrian alabasters, those found at Nimroud as well as those from Khorsabad, "the great king" is furnished with the same appendage of royalty, a slender rod, but destitute of any knob or ornament. On the Khorsabad reliefs the rod is painted red, doubtless to represent gold; proving that "the golden sceptre" was a simple wand of that precious metal, commonly held in the right hand, with one end resting on the ground, and that whether the king was sitting or walking. "The gold sceptre" has received little alteration or modification since ancient times [Goss]. It was extended to Esther as a token not only that her intrusion was pardoned, but that her visit was welcome, and a favorable reception given to the suit she had come to prefer.

touched the top of the sceptre--This was the usual way of acknowledging the royal condescension, and at the same time expressing reverence and submission to the august majesty of the king.