A method to estimate mass and heat transports across hydrographic sections using hydrography together with altimetry data in a geostrophic box inverse model is presented. Absolute surface velocities computed from AVISO altimetry products made up of a combination of sea surface height measurements and geoid estimate are first compared to Ship Acoustic Doppler Current Profiler (S-ADCP) measurements of the Ovide project along hydrographic sections repeated every 2 years in summer from Portugal to Greenland. The rms difference between S-ADCP and altimetry velocities averaged on distances of about a hundred km accounts to 3.3 cm s−1. Considering that the uncertainty of S-ADCP velocities is found at 1.5 cm s−1, altimetry errors are estimated at 3 cm s−1. Transports across Ovide sections previously obtained using S-ADCP data to constrain the geostrophic inverse box model are used as reference. The new method is found useful to estimate absolute transports across the sections, as well as part of their variability. Despite associated uncertainties about 50% larger than when S-ADCP is used, our results for the North Atlantic Current and heat transports, with uncertainties of 10 to 15%, reproduce the variability already observed. The largest uncertainties are found in the estimates of the East Greenland Irminger Current (EGIC) transport (30%), induced by larger uncertainties associated with altimetry data at the western boundary.