The growing ecosystem of Web APIs and IoT devices enables us to create a mashup within a short period of time. However, it is difficult to find appropriate Web APIs and IoT devices. Moreover, investigating a combination of Web APIs and IoT devices is much more difficult. The growing ecosystem enables us to achieve ideas in alternative ways, although it is difficult to find such alternative ways. We propose a recommendation system that takes the quality characteristics and such alternative ways into account. The system is implemented using a Steiner tree approximation algorithm, which can recommend a combination of Web APIs and IoT devices suitable for mashups. We tested the system in two aspects, i.e., the validity and performance of the algorithm. The validity was proved by running the system against a graph of actual Web APIs and IoT devices. The performance was proved by running the system against large graphs generated using a pseudorandom number generator. The system can output a result within 8 s against 28,200 nodes and five terminals, which is a considerably shorter time than that required by skilled developers to come up with a combination.