Results from an experimental study of the collisionless interaction of two laser-produced plasmas in a magnetic field with applications to supernova remnant shock physics are presented. The dynamics of the two plasmas and their interaction are studied with and without magnetic field through spatially and temporally resolved measurements of the electron density. Experimental results show that counter-propagating collisionless plasmas interpenetrate when no magnetic field is present. In contrast, results obtained with the addition of a 7.5 T magnetic field perpendicular to plasma flow show density features in the interaction area that only occur when the field is present. The reason for this remains uncertain. It is suggested that this results from an increase in the effective collisionality as the magnetic field reduces the ion and electron gyroradius below the size of the experiment.