The Gaia mission is delivering a large number of astrometric orbits for binary stars. By combining these with spectroscopic orbits for systems with two observable spectra (SB2), it is possible to derive the masses of both components. However, to get masses with a good accuracy requires accurate spectroscopic orbits, which is the major aim of the present paper. A subsidiary aim is to discover SB2 systems hiding among known SB1, and even though this search may often prove unsuccessful, the acquired radial velocities may be used anyway to improve the existing spectroscopic orbits.New radial velocities for 58 binary systems from the Catalogue of Spectroscopic Binary Orbits (SB9), obtained using the high-resolution HERMES spectrograph installed on the 1.2m Mercator telescope, were used to possibly identify hitherto undetected SB2 systems. For SB1 systems with inaccurate orbits, these new radial-velocity measurements were used to improve the orbital accuracy. This paper provides 51 orbits (41 SB1 and 10 SB2) that have been improved with respect to the solution listed in the SB9 catalogue, out of the 58 SB9 orbits studied, which belong to 56 stellar systems. Among them, there are five triple and four quadruple systems. Despite the high resolution of HERMES, HIP 115142 A is the only system which we detected as a new SB2 system. The B component of the visual binary HIP 92726 has now been found to be a spectroscopic system as well, which makes HIP 92726 a newly discovered quadruple system (SB1+SB1). The high HERMES resolution allowed us moreover to better isolate the signature of the secondary component of HIP 12390, HIP 73182 and HIP 111170. More accurate masses have thus been derived for them. Among the 30 SB also present in Gaia Data Rlease 3 (DR3) and with periods shorter than the Gaia DR3 time span (~1000d), only 5 where flagged as binaries by DR3. Various DR3 selection criteria are responsible for this situation.