Hot stamping dies include cooling channels to treat the formed sheet. The optimum cooling channels of dies and molds should adapt to the shape and surface of the dies, so that a homogeneous temperature distribution and cooling are guaranteed. Nevertheless, cooling ducts are conventionally manufactured by deep drilling, attaining straight channels unable to follow the geometry of the tool. Laser Metal Deposition (LMD) is an additive manufacturing technique capable of fabricating nearly free-form integrated cooling channels and therefore shape the so-called conformal cooling. The present work investigates the design and manufacturing of conformal cooling ducts, which are additively built up on hot work steel and then milled in order to attain the final part. Their mechanical performance and heat transfer capability has been evaluated, both experimentally and by means of thermal simulation. Finally, conformal cooling conduits are evaluated and compared to traditional straight channels. The results show that LMD is a proper technology for the generation of cooling ducts, opening the possibility to produce new geometries on dies and molds and, therefore, new products.