Plan on moving your Limelight hydrangea before new growth begins, either in late winter or early spring.
Prepare a new location where the hydrangea is exposed to filtered sunlight, or to morning sun and afternoon shade. Avoid full shade because the shrub won't bloom. Avoid bright, direct sunlight, which is too hot. Placing your hydrangea in an overly sunny spot may cause the shrub to wilt and will require more watering.
Cultivate the planting area to a depth of 10 to 12 inches using a shovel or tiller, then work in 2 to 3 inches of compost or well-rotted manure. Cultivation and addition of organic material is especially critical if the soil is poor or compacted.
Dig a hole in the new location. Make the hole two to three times the width of the hydrangea's root ball, but no deeper than the height of the root ball.
Tie a rope or string loosely around the shrub if the hydrangea is large, as tying the branches keeps them out of the way and prevents breakage.
Dig a wide circle around the hydrangea in its current location. Dig deeply, retaining as much of the shrub's root ball as possible, then lift the shrub carefully from the ground.
Place the shrub on a tarp or a piece of cardboard. Transplant the hydrangea as soon as possible. If you aren't ready to transplant, place the shrub in the shade and keep the root ball moist.
Place the hydrangea in the new hole. Adjust the depth of the hole as necessary, as the planting depth must be the same as the shrub's previous planting depth. Fill in around the root ball with the removed soil.
Water the hydrangea deeply. Keep the soil consistently moist the first year. Thereafter, water the shrub as needed during hot, dry weather.