Aims. We present a detailed multi-wavelength study of four new supernova remnants (SNRs) in the Large Magellanic Cloud (LMC). The objects were identified as SNR candidates in X-ray observations performed during the survey of the LMC with XMM-Newton. Methods. Data obained with XMM-Newton are used to investigate the morphological and spectral features of the remnants in X-rays. We measure the plasma conditions, look for supernova (SN) ejecta emission, and constrain some of the SNR properties (e.g. age and ambient density). We supplement the X-ray data with optical, infrared, and radio-continuum archival observations, which allow us to understand the conditions resulting in the current appearance of the remnants. Based on the spatially-resolved star formation history (SFH) of the LMC together with the X-ray spectra, we attempt to type the supernovae that created the remnants. Results. We confirm all four objects as SNRs, to which we assign the names MCSNR J0508−6830, MCSNR J0511−6759, MCSNR J0514−6840, and MCSNR J0517−6759. In the first two remnants, an X-ray bright plasma is surrounded by very faint [S ii] emission. The emission from the central plasma is dominated by Fe L-shell lines, and the derived iron abundance is greatly in excess of solar. This establishes their type Ia (i.e. thermonuclear) SN origin. They appear to be more evolved versions of other Magellanic Cloud iron-rich SNRs which are centrally-peaked in X-rays. From the two other remnants (MCSNR J0514−6840 and MCSNR J0517−6759), we do not see ejecta emission. At all wavelengths at which they are detected, the local environment plays a key role in their observational appearance. We present evidence that MCSNR J0517−6759 is close to and interacting with a molecular cloud, suggesting a massive progenitor.