The Isotope and Muon Production using Advanced-Cyclotron and Target Technology Project (IMPACT) foresees the introduction of two new target stations and three new beamlines: one for radionuclide production and two for surface muon production. The latter forms the project, High-Intensity Muon Beams (HIMB), which plans to increase the muon rate from the current world record of 10⁸ μ⁺/s up to 10¹⁰ μ⁺/s. This work presents an overview of the future HIMB beamlines focusing on the magnet designs that have been developed to ensure increased muon rate production and transmission. Specific radiation-hard resistive coils, based on mineral insulation, are required in this case due to the proximity to the target station. A high muon capture and transmission efficiency requires solenoid-like magnets, as well as dipole magnets and crossed-field separators to select the desired particles, while suppressing unwanted background particles. The radiation-hard capture solenoid plays the most important role in the whole beamline since it must provide a high capture efficiency. Beam optics studies provided the on-axis field profile necessary for optimizing the size and shape of the capture solenoid. Therefore, the paper will also elucidate on these solenoid design strategies for achieving the desired capture efficiency.