Recent low-temperature laboratory measurements and astronomical observations have proved that the fullerene cation C-60(+) is responsible for four diffuse interstellar bands (DIBs). These absorptions correspond to the strongest bands of the lowest electronic transition. The gas phase spectrum below 10 K is reported here for the full wavelength range encompassed by the electronic transition. The absorption spectrum of C-70(+), with its origin band at 7959.2 angstrom, has been obtained under similar laboratory conditions. Observations made toward the reddened star HD 183143 were used in a specific search for the absorption of these fullerene cations in diffuse clouds. In the case of C-60(+), one further band in the astronomical spectrum at 9348.5 angstrom is identified, increasing the total number of assigned DIBs to five. Numerous other C-60(+) absorptions in the laboratory spectrum are found to lie below the astronomical detection limit. Special emphasis is placed on the laboratory determination of absolute absorption cross-sections. For C-60(+) this directly yields a column density, N(C-60(+)), of 2 x 10(13) cm(-2) in diffuse clouds, without the need to rely on theoretical oscillator strengths. The intensity of the C-70(+) electronic transition in the range 7000-8000 angstrom is spread over many features of similar strength. Absorption cross-section measurements indicate that even for a similar column density, the individual absorption bands of C-70(+) will be too weak to be detected in the astronomical spectra, which is confirmed giving an upper limit of 2 m angstrom to the equivalent width.