In the framework of the design activities conducted in the EU for dimensioning the future fusion demonstration reactor (DEMO), extensive analyses were carried out within the framework of the EUROfusion consortium, with the objective of defining the design of the DEMO magnets system. To this aim, CEA has developed ad-hoc predimensioning tools and associated methods in order to size the different magnets: toroidal field coils, central solenoid (CS) and poloidal field (PF) coils. Once predimensioned, the magnet concepts undergo a detailed evaluation procedure with more complex tools and methods. As these detailed analyses are time consuming, the whole design process benefits from an accurate and robust predimensioning process. The predimensioning tools described herein address various aspects driving the operational limits of the magnets while energized in the tokamak, related to electromagnetic, thermal, and mechanic phenomena. In this paper, we expose the latest developments in the predimensioning tools and the methods employed for obtaining a rapid and reliable macroscopic semi-analytical representation of the magnets. The assessment of the predimensioning tools on reference configurations (e.g., ITER) is also described. The application of these design tools on the DEMO configuration issued by EUROfusion is presented, and the resulting magnet design proposals are summarized: First, the PF system, composed of six coils, with one PF selected for study here. Second, the CS, with a modular geometry (five modules) and pancake winding. The approach here assesses the resilience of the CS to a fast-transient (breakdown). The outcomes of a sensitivity study on parameters/criteria are discussed, and extended to some tentative recommendations on the design approach for the DEMO PF and CS magnets. For the PF, a design is obtained for the PF5 coil following a dimensioning methodology consistent with the ITER PF system design with the same level of definition of the plasma operating scenario. As for the CS, it is stressed that consideration of the internal field (from shielding) substantially affects temperature margin results.