Methods for forming cutting elements comprising polycrystalline materials, methods for forming polycrystalline compacts for cutting elements of a drilling tool, methods for forming polycrystalline diamond compacts, and resulting polycrystalline compacts and cutting elements are disclosed. Grains of a hard material are introduced to a press and subjected to a high-pressure, high-temperature (HPHT) process to sinter the grains. The system conditions (i.e., temperature and pressure) are then adjusted past a phase or state change point, after which, at least one of the system conditions is held during an anneal stage before the system conditions are adjusted to final levels. The resulting compacts and cutting elements may therefore include inter-granularly bonded hard material grains with a more stable microstructure (e.g., less stressed microstructure) than a polycrystalline compact and cutting element formed without an anneal stage during the HPHT process.