We present a combined multimethod experimental and theoretical study of the geometric and electronic properties of Co-tetraphenyl-porphyrin (Co-TPP) molecules adsorbed on a Ag(111) surface. Scanning tunneling microscopy (STM) topographs reveal that Co-TPP forms highly regular arrays with a square unit cell. Hereby, the Co-TPP molecules do not occupy a unique adsorption site on the Ag(111) atomic lattice. The central Co atom of the Co-TPP is found to reside predominantly above fcc and hcp hollow sites of the substrate, as determined from the photoelectron diffraction patterns. A strong adsorption-induced deformation of Co-TPP involving a saddle-shaped macrocycle is evidenced by high-resolution STM images and quantified by near-edge x-ray absorption fine-structure measurements. By scanning tunneling spectroscopy we resolved discrete molecular electronic states and mapped the pertaining spatial charge-density distribution. Specifically, we discuss the interaction of orbitals originating from the Co-metal center with the porphyrin macrocycle and show that the varying adsorption sites induce a modulation in the Co-TPP lowest unoccupied molecular orbital. These findings are corroborated by density-functional-theory calculations.