A mechanical garment press assembly enables users to mechanically press garments during travel and may be stored or carried in combination with standard carry-on luggage. The garment press assembly comprises opposed outer resilient planar members, each of which has a hinge end and a clamp end. A hinge member flexibly interconnects the hinge ends. Clamping structure clamps the clamp ends toward one another after a (wrinkled) garment section is received intermediate the opposed outer planar members for imparting primary wrinkle-removing forces into the target garment section. Tension members interconnect the hinge ends to the clamp ends and retain the resilient members is bowed tension for imparting secondary wrinkle-removing forces into the target garment section. Various portable assemblies are contemplated based on the foregoing basics as well as a home-based version. Certain garment pressing methods are also described based on the foregoing basics.