We have measured the Sunyaev-Zel'dovich (SZ) effect for a sample of 10 strong lensing selected galaxy clusters using the Sunyaev-Zel'dovich Array (SZA). The SZA is sensitive to structures on spatial scales of a few arcminutes, while the strong lensing mass modeling constrains the mass at small scales (typically <30''). Combining the two provides information about the projected concentrations of the strong lensing clusters. The Einstein radii we measure are twice as large as expected given the masses inferred from SZ scaling relations. A Monte Carlo simulation indicates that a sample randomly drawn from the expected distribution would have a larger median Einstein radius than the observed clusters about 3% of the time. The implied overconcentration has been noted in previous studies and persists for this sample, even when we take into account that we are selecting large Einstein radius systems, suggesting that the theoretical models still do not fully describe the observed properties of strong lensing clusters.