  Previous studies on the rotation of Sun-like stars revealed that the
rotational rates of young stars converge towards a well-defined evolution that
follows a power-law decay. It seems, however, that some binary stars do not
obey this relation, often by displaying enhanced rotational rates and activity.
In the Solar Twin Planet Search program we observed several solar twin
binaries, and found a multiplicity fraction of $42\% \pm 6\%$ in the whole
sample; moreover, at least three of these binaries (HIP 19911, HIP 67620 and
HIP 103983) clearly exhibit the aforementioned anomalies. We investigated the
configuration of the binaries in the program, and discovered new companions for
HIP 6407, HIP 54582, HIP 62039 and HIP 30037, of which the latter is orbited by
a $0.06$ M$_\odot$ brown dwarf in a 1-month long orbit. We report the orbital
parameters of the systems with well-sampled orbits and, in addition, the lower
limits of parameters for the companions that only display a curvature in their
radial velocities. For the linear trend binaries, we report an estimate of the
masses of their companions when their observed separation is available, and a
minimum mass otherwise. We conclude that solar twin binaries with low-mass
stellar companions at moderate orbital periods do not display signs of a
distinct rotational evolution when compared to single stars. We confirm that
the three peculiar stars are double-lined binaries, and that their companions
are polluting their spectra, which explains the observed anomalies.
