Experimental 103Rh NMR chemical shifts of mono- and binuclear rhodium(I) complexes containing s- or as-hydroindacenide and indacenediide bridging ligands with different ancillary ligands (1,5-cyclooctadiene, ethylene, carbonyl) are presented. A protocol, based on density functional theory calculations, was established to determine 103Rh NMR shielding constants in order to rationalise the effects of electronic and structural variations on the spectroscopic signal, and to gain insight into the efficiency of this computational method when applied to organometallic systems. Scalar and spin-orbit relativistic effects based on the ZORA (zeroth order regular approximation) level have been taken into account and discussed. A good agreement was found for model compounds over a wide range of chemical shifts of rhodium (approximately 10,000 ppm). This allowed us to discuss the experimental and calculated delta(103Rh) in larger complexes and to relate it to their electronic structure.