A Viking-style tarred shield can be made as a historical craft object by applying a restrained pine tar finish to suitable wooden parts, while keeping the shield safe, dry, and structurally sound.
A tarred shield is usually a reenactment or display interpretation rather than a single fixed historical formula. Tar can darken timber, give a weathered appearance, and help protect the wood from damp. It is most relevant to the wooden back, rim components, or intentionally rustic surfaces rather than clean painted decoration.
Use dry timber and test the finish before treating the whole shield. Pine tar can darken unevenly across planks, end grain, leather edging, linen facing, and painted areas. If the shield has decorative paint, tar may stain it permanently. If the shield has rawhide or leather, the tar can change the colour, feel, and smell.
A shield used for reenactment combat has safety needs beyond appearance. Tar should not hide cracks, loose boards, failing bosses, or damaged grips. For a display shield, the finish can be chosen for atmosphere. For an object that will be struck, construction and inspection matter more than the surface colour.