Ocean observing systems in coastal, shelf and marginal seas collect diverse oceanographic information supporting a wide range of socioeconomic needs, but observations are necessarily sparse in space and/or time due to practical limitations. Ocean analysis and forecast systems capitalize on such observations, producing data-constrained, four-dimensional oceanographic fields. Here we review efforts to quantify the impact of ocean observations, observing platforms, and networks of platforms on model products of the physical ocean state in coastal regions. Quantitative assessment must consider a variety of issues including observation operators that sample models, error of representativeness, and correlated uncertainty in observations. Observing System Experiments, Observing System Simulation Experiments, representer functions and array modes, observation impacts, and algorithms based on artificial intelligence all offer methods to evaluate data-based model performance improvements according to metrics that characterize oceanographic features of local interest. Applications from globally distributed coastal ocean modeling systems document broad adoption of quantitative methods, generally meaningful reductions in model-data discrepancies from observation assimilation, and support for assimilation of complementary data sets, including subsurface in situ observation platforms, across diverse coastal environments.