He was awarded the Royal Society's Hughes medal in 1936 for his discovery of the Schrot effect (spontaneous current variations in high-vacuum discharge tubes, called by him the "Schrot effect": literally, the "small shot effect") in thermionic emission and his invention of the screen-grid tetrode and a superheterodyne method of receiving wireless signals.
In 1964 he received the Werner-von-Siemens-Ring honoring his ground-breaking work on the physical understanding of many phenomena that led to many important technical appliances, among them tube amplifiers and semiconductors.
Note: The invention of superheterodyne is usually attributed to Edwin Armstrong. However, Schottky published an article in Proc. IRE that he had also invented something similar.
Walter Schottky Institute (Germany) was named after him.