Marine magnetotelluric measurements using free-fall'' instruments without effective compasses suffer from the problem of unknown orientation of the receivers at the seafloor. While past works indicate that marine magnetotelluric orientation of the instruments can be estimated by reference to land deployments of known orientation using the transfer tensor method, there is limited published information on how this is implemented in practice. We document this method and propose a set of new time- and frequency-domain approaches to solve this orientation problem of the seafloor receivers. We test these methodologies in onshore and offshore magnetotelluric data whose orientations are well known and apply these techniques to marine magnetotelluric data with unknown orientation. For the controlled tests, both time- and frequency-domain approaches produce overall comparable results. To investigate the effects of the subsurface structure distribution on the orientation process, a dimensionality analysis of a controlled dataset is carried out. In subsequent analysis using the available disoriented marine magnetotelluric data from offshore Brazil and from the Vassouras magnetic observatory on the mainland for remote referencing, frequency-domain methods yield approximate orientation angles among themselves with low standard deviation each. Time-domain results are consistent for most cases but differ from frequency-domain results for some situations.