In this contribution, which is the second paper in a series, we report on the design and development of several pieces of equipment, which facilitate the preparation of a hemispherical single crystal with a desired crystallographic surface structure starting with a spherical Pt single crystal. The pieces of equipment include a dual, high-resolution charge-coupled device (CCD)-based camera for acquiring Laue X-ray back-scattering patterns to orient spherical single crystals, a precision custom-designed jig for cutting and polishing pre-oriented single crystals, and an induction annealing system with controlled gaseous atmosphere for obtaining well-ordered and defect-free single crystal surfaces. Firstly, the paper describes the dual CCD camera setup, which allows acquiring, processing, and analyzing Laue back-scattering patterns in a digital format. The single crystal holder comprising a goniometer, the CCD-based detection system, and an optomechanical system together allow simple, adaptable, quick, and accurate single crystal orientation. Secondly, the paper presents details of a high-precision jig used in the cutting and polishing of single crystals. The jig setup includes a goniometer supporting a holder in which a single crystal is mounted and two micrometers. It maintains the desired single crystal surface parallel to the polishing disk on which abrasive materials are dispersed and polishing cloths are mounted. The micrometers allow monitoring the polishing rate and maintaining the desired single crystal surface exactly parallel to the polishing disk. Thirdly, the paper describes details of the annealing system. It consists of an induction-annealing furnace with a custom-made coil, a custom-designed quartz cell that facilitates single crystal annealing under controlled atmosphere conditions. Optimization of the induction annealing parameters and conditions, which determine the final quality of single crystal surfaces, is described in detail. Finally, the paper explains the unique aspects of this setup and methodically describes the operating procedures required to obtain a hemispherical single crystal with an atomically flat surface.