In this paper we analyse the material coherence of oceanic eddies sampled by ships during 9 oceanographic campaigns, 8 of which were conducted in the Atlantic Ocean (EUREC4A-OA, M124, MSM60, MSM74, M160, HM2016611, KB2017606, KB2017618) and one in the Indian Ocean (Physindien 2011). After reviewing previous definitions of coherence, we perform a relative error analysis of our data. To identify the eddy cores and assess the material coherence of the well-sampled eddies (19 out of 28 eddies in total), we use criteria based on active tracers (potential vorticity, temperature, salinity). The maximum tracer anomaly is often below the pycnocline (below the frequency stratification maximum). Therefore, some eddies are not considered to be materially coherent using only surface data, whereas they are when we study their three-dimensional structure. Two methods are then presented to extrapolate eddy volumes from a single ship section. The horizontal and vertical resolutions of the data are critical for this determination. Our results show that the outermost closed contour of the Brunt-Vaisala frequency is a good approximation for the materially coherent eddy core to determine the eddy volume.