* 1950. Awarded the Corday-Morgan medal and Prize of the Chemical Society.
* 1955. Awarded the H G Smith Medal of the Royal Australian Chemical Institute.
* 1959. Elected Fellow of the Royal Society.
* 1959. Awarded the Royal Medal of the Royal Society of New South Wales.
* 1959. Elected Corresponding Member of the Finnish Chemical Society.
* 1961. Appointed Tilden Lecturer of the Chemical Society.
* 1967. Appointed Liversidge Lecturer of the Chemical Society.
* 1967. Created Knight Bachelor for services to science in the 1967 Birthday Honours.
* 1968. Awarded the Gold Medal of the Italian Chemical Society.
* 1968. Honorary Doctor of Science, University of East Anglia.
* 1968. Honorary Doctor of Science, City University, London.
* 1969. Awarded the Sigillum Magnum Medal, University of Bologna.
* 1969. Honorary Doctor of Science, University of New South Wales.
* 1971. Elected Honorary Member of the Accademia Peloritana (Sicily)
The Nyholm Prize for Inorganic Chemistry and the Nyholm Prize for Education, founded by the Chemical Society in 1973, are now awarded biennially by the Royal Society of Chemistry.
The mineral Nyholmite is named after Nyholm. It was discovered in Broken Hill in 2009 and its structure was elucidated by Elliot et al.