Context. In the last five years the Fermi Large Area Telescope (LAT) instrument detected GeV γ-ray emission from five novae. The GeV emission can be interpreted in terms of an inverse Compton process of electrons accelerated in a shock. In this case it is expected that protons in the same conditions can be accelerated to much higher energies. Consequently they may produce a second component in the γ-ray spectrum at TeV energies. Aims: We aim to explore the very high-energy domain to search for γ-ray emission above 50 GeV and to shed light on the acceleration process of leptons and hadrons in nova explosions. Methods: We have performed observations, with the MAGIC telescopes of the classical nova V339 Del shortly after the 2013 outburst; optical and subsequent GeV γ-ray detections triggered the MAGIC observations. We also briefly report on VHE observations of the symbiotic nova YY Her and the dwarf nova ASASSN-13ax. We complement the TeV MAGIC observations with the analysis of contemporaneous Fermi-LAT data of the sources. The TeV and GeV observations are compared in order to evaluate the acceleration parameters for leptons and hadrons. Results: No significant TeV emission was found from the studied sources. We computed upper limits on the spectrum and night-by-night flux. The combined GeV and TeV observations of V339 Del limit the ratio of proton to electron luminosities to Lp ≲ 0.15 Le. Appendix A is available in electronic form at http://www.aanda.org