Magnetic resonance electrical properties tomography is a type of quantitative magnetic resonance imaging that aims to reconstruct the conductivity and permittivity of biological tissue. These electrical properties of the tissue can be used to compute the specific absorption rate, to differentiate tumours from healthy tissue and for hyperthermia treatment planning. Several methods to reconstruct these electrical properties exist with different degrees of success. Combining analytical reconstruction methods with deep learning methods is left relatively unexplored in the field of magnetic resonance electrical properties tomography. Hence, this work explores such hybrid methods in which deep learning is embedded in an analytical reconstruction method. A recurrent inference machine is integrated into the iterative reconstruction scheme called Contrast Source Inversion, in an attempt to decrease its high computational load. Additionally, a U-net is trained to correct reconstructed conductivity maps using discrepancies in measured- and reconstructed phase data, which is based on the relation between conductivity and phase in the Helmholtz equation. The recurrent inference machine embedded version of contrast source inversion failed to achieve a desirable reconstruction quality with its current implementation. However, the large amount of potential improvements to its implementation motivates further research into its application before discarding it. The conductivity correction U-net is able to correct conductivity errors as small as 0.13 S/m when used iteratively or 0.05 S/m when used a single time when noiseless data is used. Further research in its capabilities of handling noisy data is required to assess practical usage.