FIG. 1 is a front perspective view showing a “handle for article of cookware” incorporating the design of my invention; FIG. 2 is a top view thereof; FIG. 3 is a bottom view thereof; FIG. 4 is a side view thereof; FIG. 5 is another side view thereof; FIG. 6 is a front view thereof; FIG. 7 is a rear view thereof; FIG. 8 is a front perspective view showing the handle shown in FIG. 1 embodied in a different article of cookware; FIG. 9 is a top view of the handle shown in FIG. 8; FIG. 10 is a bottom view of the handle shown in FIG. 8; FIG. 11 is a side view of the handle shown in FIG. 8; FIG. 12 is another side view of the handle shown in FIG. 8; FIG. 13 is a front view of the handle shown in FIG. 8; and, FIG. 14 is a rear view of the handle shown in FIG. 8. The part of the drawings shown in phantom lines depicts the environment of my new design and forms no part of my design.