Hydrogen bonding has a ubiquitous role in electron transport and in molecular recognition, with DNA base pairing being the best-known example. Scanning tunnelling microscope images and measurements of the decay of tunnel current as a molecular junction is pulled apart by the scanning tunnelling microscope tip are sensitive to hydrogen-bonded interactions. Here, we show that these tunnel-decay signals can be used to measure the strength of hydrogen bonding in DNA base pairs. Junctions that are held together by three hydrogen bonds per base pair (for example, guanine-cytosine interactions) are stiffer than junctions held together by two hydrogen bonds per base pair (for example, adenine-thymine interactions). Similar, but less pronounced effects are observed on the approach of the tunnelling probe, implying that attractive forces that depend on hydrogen bonds also have a role in determining the rise of current. These effects provide new mechanisms for making sensors that transduce a molecular recognition event into an electronic signal.