During development and wound healing, cells need to form long-range ordered structures to ensure precise formation of organs and repair damage. This requires cells to locate specific partner cells to which to adhere. How such cell matching reliably happens is an open problem, particularly in the presence of biological variability. Here, we use an equilibrium energy model to simulate how cell matching can occur with subcellular precision. A single parameter-encapsulating the competition between selective cell adhesion and cell compressibility-can reproduce experimental observations of cell alignment in the Drosophila embryonic heart. This demonstrates that adhesive differences between cells (in the case of the heart, mediated by filopodia interactions) are sufficient to drive cell matching without requiring cell rearrangements. The biophysical model can explain observed matching defects in mutant conditions and when there is significant biological variability. Using a dynamic vertex model, we demonstrate the existence of an optimal range of effective cell rigidities for efficient matching. Overall, this work shows that equilibrium energy considerations are consistent with observed cell matching in cardioblasts and has potential application to other systems, such as neuron connections and wound repair.