In this paper, we present the design of a Constrained Application Protocol (CoAP) proxy able to interconnect Web applications based on Hypertext Transfer Protocol (HTTP) and WebSocket with CoAP based Wireless Sensor Networks. Sensor networks are commonly used to monitor and control physical objects or environments. Smart Cities represent applications of such a nature. Wireless Sensor Networks gather data from their surroundings and send them to a remote application. This data flow may be short or long lived. The traditional HTTP long-polling used by Web applications may not be adequate in long-term communications. To overcome this problem, we include the WebSocket protocol in the design of the CoAP proxy. We evaluate the performance of the CoAP proxy in terms of latency and memory consumption. The tests consider long and short-lived communications. In both cases, we evaluate the performance obtained by the CoAP proxy according to the use of WebSocket and HTTP long-polling.