In this article, we present a feature-based remote sensing (RS) image matching method termed progressive motion coherence (PMC). We formulate the matching problem into a mathematical model and derive a closed-form solution. The objective function is only based on two novel coherence constraints, namely, efficient neighborhood element coherence and relative order-aware motion coherence, and hence, it is general enough and can be applied to RS image matching with different image types and degradations. The efficient neighborhood element coherence uses the Jaccard distance to measure the dissimilarity of two neighborhoods, which are lists composed of $k$ nearest neighbors of feature points. To prevent overpenalization on the outliers, we combine it with an exponential function, which is simple yet efficient. The relative order-aware motion coherence is an alternative to motion smoothness, which is based on the observation that the relative order of neighboring matches for inliers in a small region can be well preserved, while for outliers, the relative order changes greatly. The above two coherences are robust to large rotation changes and low ratio inliers. Extensive experiments on five RS image datasets compared with seven state of the arts demonstrate that our PMC is more efficient and robust than the competitors.