Metal-organic frameworks (MOFs) with nodes consisting of zirconium oxide clusters (Zr) offer new opportunities as supports for catalysts with well-defined, essentially molecular, structures. We used the precursor Rh(CH)(acac) (acac is acetylacetonate) to anchor Rh(I) complexes to the nodes of the MOF UiO-67 and, for comparison, to the zeolite dealuminated HY (DAY). These were characterized experimentally by measurement of catalytic activities and selectivities for ethylene hydrogenation and dimerization in a once-through flow reactor at 298 K and 1 bar. The catalyst performance data are complemented with structural information determined by infrared and extended X-ray absorption fine structure spectroscopies and by calculations at the level of density functional theory, the latter carried out also to extend the investigation to a related MOF, NU-1000. The agreement between the experimental and calculated structural metrics is good, and the calculations have led to predictions of reaction mechanisms and associated energetics. The data demonstrate a correlation between the catalytic activity and selectivity and the electron-donor tendency of the supported rhodium (as measured by the frequencies of CO ligands bonded as probes to the Rh(I) centers), which is itself a measure of the electron-donor tendency of the support.