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 survey 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 ˜7, and for V1095 Sco by a factor of ˜3. We detect significant circular polarization 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 α 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.