Close M dwarf binaries and higher multiples allow the investigation of rotational evolution and mean magnetic flux unbiased from scatter in inclination angle and age since the orientation of the spin axis of the components is most likely parallel and the individual systems are coeval. Systems composed of an early-type (M0.0–M4.0) and a late-type (M4.0–M8.0) component offer the possibility to study differences in rotation and magnetism between partially and fully convective stars. We have selected 10 of the closest dM systems to determine the rotation velocities and the mean magnetic field strengths based on spectroscopic analysis of FeH lines of Wing–Ford transitions at 1 μm observed with Very Large Telescope/CRIRES. We also studied the quality of our spectroscopic model regarding atmospheric parameters including metallicity. A modified version of the Molecular Zeeman Library (MZL) was used to compute Landég-factors for FeH lines. Magnetic spectral synthesis was performed with the synmast code. We confirmed previously reported findings that less massive M dwarfs are braked less effectively than objects of earlier types. Strong surface magnetic fields were detected in primaries of four systems (GJ 852, GJ 234, LP 717−36 and GJ 3322), and in the secondary of the triple system GJ 852. We also confirm strong 2-kG magnetic field in the primary of the triple system GJ 2005. No fields could be accurately determined in rapidly rotating stars with υ sin i > 10 km s−1. For slowly and moderately rotating stars, we find the surface magnetic field strength to increase with the rotational velocity υ sin i which is consistent with other results from studying field stars.