Example tapered nut valve plug fastener apparatus disclosed herein include a valve stem, a first nut, a valve plug, and a second nut. The first nut includes a first tapered surface and the second nut includes a second tapered surface. The valve plug includes a bore. The first nut threadably engages the valve stem and the valve stem passes through the bore. The bore engages the first tapered surface. The second nut threadably engages the valve stem and the bore engages the second tapered surface.