Flexible polymers, most notable poly(ethylene glycol), are commonly grafted to drug-carrying liposomes and nanoparticles to increase circulation time in vivo and extend the reach of targeting moieties. In this work we develop a model for the specific bridging and non-specific steric forces imparted by such polymer coatings towards model receptor surfaces. Using direct experimental measurements we highlight the applicability of this modeling approach. The model is in good agreement with measurements made with the Surface Forces Apparatus. The experiments and model suggest the existence of an optimal polymer architecture for adhering to target cells. Although relatively little is known about the structure of endothelial glycocalyx, conservative approximations of repulsion from glycocalyx of several hypothetical thicknesses suggest that it may dramatically decrease targeting efficacy. We use the model to show that the optimum architecture is likely to depend on the thickness of the targeted cell's glycocalyx.