The answer depends on whether the electromagnetic wave is linearly or circularly polarized.
The picture below is a description of the phase relationship between the electric and magnetic field components of a linearly polarized classical electromagnetic wave.
The electric and magnetic field components of a linearly polarized electromagnetic wave oscillate in such a way that they peak at the same time and they become zero at the same time but they point to different directions in space (separated by an angle of 90 degrees) (electric and magnetic field components are orthogonal waves) as shown in the figure above.
Phase difference refers to time difference. Since there is no time difference between the peaks of the electric and magnetic oscillations the phase difference between the electric and magnetic field vectors of a linearly polarized electromagnetic wave is zero. A 3D animation of a linearly polarized electromagnetic wave is shown below.
The circularly polarized wave can be expressed as two linearly polarized waves, shifted by 90° in phase and rotated by 90° in polarization. If you pick some direction to measure the fields along, the components of E and B along that direction have a 90° phase shift with respect to each other. A phase shift of 90° means that as E peaks B becomes zero, and as B peaks E becomes zero.
In order to get more intuition about linearly polarized as well as circularly polarized orthogonal waves please see the video below