  We present a detailed analysis of high-resolution spectropolarimetric
observations of the weak-line T Tauri stars (wTTSs) TWA 9A and V1095 Sco as
part of a wider sur- vey of magnetic properties and activity in weak-line T
Tauri stars, called MaTYSSE (Magnetic Topologies of Young Stars and the
Survival of close-in giant Exoplanets). Our targets have similar masses but
differing ages which span the stage of radiative core formation in solar-mass
stars. We use the intensity line profiles to reconstruct surface brightness
maps for both stars. The reconstructed brightness maps for TWA 9A and V1095 Sco
were used to model and subtract the activity-induced jitter, reducing the RMS
in the radial velocity measurements of TWA 9A by a factor of $\sim$7, and for
V1095 Sco by a factor of $\sim$3. We detect significant circular polarisation
for both stars, but only acquired a high quality circular polarisation
time-series for TWA 9A. Our reconstructed large-scale magnetic field
distribution of TWA 9A indicates a strong, non-axisymmetric field. We also
analyse the chromospheric activity of both stars by investigating their
H$\alpha$ emission, finding excess blue-ward emission for most observations of
V1095 Sco, and symmetric, double-peaked emission for TWA 9A, with enhanced
emission at one epoch likely indicating a flaring event.
