Aims. We present a multi-wavelength analysis of the evolved supernova remnants MCSNR J0506−7025 and MCSNR J0527−7104 in the Large Magellanic Cloud. Methods. We used observational data from XMM-Newton, the Australian Telescope Compact Array, and the Magellanic Cloud Emission Line Survey to study their broad-band emission and used Spitzer and H i data to gain a picture of the environment into which the remnants are expanding. We performed a multi-wavelength morphological study and detailed radio and X-ray spectral analyses to determine their physical characteristics. Results. Both remnants were found to have bright X-ray cores, dominated by Fe L-shell emission, which is consistent with reverse shock-heated ejecta with determined Fe masses in agreement with Type Ia explosion yields. A soft X-ray shell, which is consistent with swept-up interstellar medium, was observed in MCSNR J0506−7025, suggestive of a remnant in the Sedov phase. Using the spectral fit results and the Sedov self-similar solution, we estimated the age of MCSNR J0506−7025 to be ~16−28 kyr, with an initial explosion energy of (0.07−0.84) × 1051 erg. A soft shell was absent in MCSNR J0527−7104, with only ejecta emission visible in an extremely elongated morphology that extends beyond the optical shell. We suggest that the blast wave has broken out into a low density cavity, allowing the shock heated ejecta to escape. We find that the radio spectral index of MCSNR J0506−7025 is consistent with the standard −0.5 for supernova remnants. Radio polarisation at 6 cm indicates a higher degree of polarisation along the western front and at the eastern knot with a mean fractional polarisation across the remnant of P ≅ (20 ± 6)%. Conclusions. The detection of Fe-rich ejecta in the remnants suggests that both resulted from Type Ia explosions. The newly identified Fe-rich cores in MCSNR J0506−7025 and MCSNR J0527−7104 make them members of the expanding class of evolved Fe-rich remnants in the Magellanic Clouds.