We report the results of our spectropolarimetric monitoring of the weak-line T-Tauri stars ( wTTSs ) Par 1379 and Par 2244 , within the MaTYSSE ( Magnetic Topologies of Young Stars and the Survival of close-in giant Exoplanets ) programme . Both stars are of a similar mass ( 1.6 and 1.8 M \textsubscript \sun ) and age ( 1.8 and 1.1 Myr ) , with Par 1379 hosting an evolved low-mass dusty circumstellar disc , and with Par 2244 showing evidence of a young debris disc . We detect profile distortions and Zeeman signatures in the unpolarized and circularly polarized lines for each star , and have modelled their rotational modulation using tomographic imaging , yielding brightness and magnetic maps . We find that Par 1379 harbours a weak ( 250 G ) , mostly poloidal field tilted 65 \degr from the rotation axis . In contrast , Par 2244 hosts a stronger field ( 860 G ) split 3:2 between poloidal and toroidal components , with most of the energy in higher order modes , and with the poloidal component tilted 45 \degr from the rotation axis . Compared to the lower mass wTTSs , V819 Tau and V830 Tau , Par 2244 has a similar field strength , but is much more complex , whereas the much less complex field of Par 1379 is also much weaker than any other mapped wTTS . We find moderate surface differential rotation of 1.4 \times and 1.8 \times smaller than Solar , for Par 1379 and Par 2244 , respectively . Using our tomographic maps to predict the activity related radial velocity ( RV ) jitter , and filter it from the RV curves , we find RV residuals with dispersions of 0.017 kms ^ { -1 } and 0.086 kms ^ { -1 } for Par 1379 and Par 2244 , respectively . We find no evidence for close-in giant planets around either star , with 3 \sigma upper limits of 0.56 and 3.54 M \textsubscript Jup ( at an orbital distance of 0.1 au ) .