Coherent plane wave compounding is a promising technique for achieving very high frame rate imaging without compromising image quality or penetration. However, this approach relies on the hypothesis that the imaged object is not moving during the compounded scan sequence, which is not the case in cardiovascular imaging. This work investigates the effect of tissue motion on retrospective transmit focusing in coherent compounded plane wave imaging (PWI). Two compound scan sequences were studied based on a linear and alternating sequence of tilted plane waves, with different timing characteristics. Simulation studies revealed potentially severe degradations in the retrospective focusing process, where both radial and lateral resolution was reduced, lateral shifts of the imaged medium were introduced, and losses in signal-to-noise ratio (SNR) were inferred. For myocardial imaging, physiological tissue displacements were on the order of half a wavelength, leading to SNR losses up to 35 dB, and reductions of contrast by 40 dB. No significant difference was observed between the different tilt sequences. A motion compensation technique based on cross-correlation was introduced, which significantly recovered the losses in SNR and contrast for physiological tissue velocities. Worst case losses in SNR and contrast were recovered by 35 dB and 27-35 dB, respectively. The effects of motion were demonstrated in vivo when imaging a rat heart. Using PWI, very high frame rates up to 463 fps were achieved at high image quality, but a motion correction scheme was then required.