In the film, The Return of the King, Elrond delivers Andúril ready to go, and Aragorn uses the sword as he receives it. However, in the books, the Ranger ends up upgrading the housing for his heirloom as he travels — and we're not talking about some rinky-dink sheath here, either. He ends up getting a posh new scabbard, gifted to him by none other than the Lady Galadriel herself.
After the sword is reforged, the Fellowship of the Ring begins their travels, heading south, crossing through Moria, and eventually arriving in Lothlorien, where they get some much-needed rest. After spending a month in the Golden Wood, they prepare to head out again — but before they leave, Galadriel gives them all gifts. Some of these are shown in the extended edition of the film, but a few important details are left out, including the fact that she gives Aragorn a sheath specifically made for his sword.
In The Fellowship of the Ring, it states that this sheath "was overlaid with a tracery of flowers and leaves wrought of silver and gold." In addition, the name "Andúril" and the lineage of the sword are spelled out ... in gems. In other words, Aragorn doesn't just get a sheath, he gets an insanely fancy sword casing covered gold, silver, and jewels — which probably doesn't help with his reluctance to let anyone touch the darned thing whenever he takes it off.