Wireless sensor networks need very efficient network protocols due to the sensors' limited communication and computation capabilities. Network planarization - finding a planar subgraph of the network that contains all the nodes - has been a very important technique for many network protocols. It first became the foundation of various well known routing protocols, including GPSR, GOAFR and several other protocols. Since then, it has also been used in numerous other applications, including data-centric storage, network localization, topology discovery, etc. However, an important problem remains: network planarization itself is very difficult. So far, efficient planarization algorithms exist only for very restrictive models: the network must be a unit-disk graph, and accurate measurements related to the node locations (e.g., node positions or angles between adjacent links) need to be known. For more practical network models, where the transmission ranges are usually not uniform and sensors cannot obtain their accurate location information via expensive localization devices, no efficient planarization algorithm is available. In this paper, we present a novel method that robustly planarizes sensor networks of a realistic model: networks with non-uniform transmission ranges and unlocalized sensors (that is, static sensors whose locations are unknown). Our method starts with a simple shortest path between two nodes, and progressively planarizes the whole network. It achieves both efficiency and a good planarization result. We present two planarization algorithms for different settings. Our results not only solve the planarization problem, but also outperform some known results in the graph drawing research field. We demonstrate the practical performance of our method - as well as its application in topology discovery, - through extensive simulations.