Melting Temperature (Solidus)
A single, sharp melting point only really applies to very pure substances. Most materials enter a semi-molten transitional state at one temperature (solidus), and become fully liquid at another (liquidus).
Melting data is primarily useful for fabrication considerations, since mechanical properties tend to strongly deteriorate at a much lower temperature than the solidus. In metals, this deterioration is reversible on cooling, unless the material has been heat-treated or work hardened, in which case some degree of annealing is likely to have occurred.
The phenomenon of melting is generally a little too obvious to need standardized tests. However, some standards exist to cover a few challenging cases. For example, ASTM D7138 for synthetic fibers, and ASTM F766 for waxes.