To study the mechanical interface behavior of single-walled carbon nanotubes (CNTs) embedded in a noble metal, we performed CNT-metal pull-out tests with in situ scanning electron microscope experiments. Molecular dynamics (MD) simulations were conducted to predict force-displacement data during pull-out, providing critical forces for failure of the system. In MD simulations, we focused on the influence of carboxylic surface functional groups (SFGs) covalently linked to the CNT. Experimentally obtained maximum forces between 10 and 102 nN in palladium and gold matrices and simulated achievable pulling forces agree very well. The dominant failure mode in the experiment is CNT rupture, although several pull-out failures were also observed. We explain the huge scatter of experimental values with varying embedding length and SFG surface density. From simulation, we found that SFGs act as small anchors in the metal matrix and significantly enhance the maximum forces. This interface reinforcement can lead to tensile stresses sufficiently high to initiate CNT rupture. To qualify the existence of carboxylic SFGs on our CNT material, we performed analytical investigation by means of fluorescence labeling of surface species and discuss the results. With this contribution, we focus on a synergy between computational and experimental approaches involving MD simulations, nano scale testing, and analytics (1) to predict to a good degree of accuracy maximum pull-out forces of single-walled CNTs embedded in a noble metal matrix and (2) to provide valuable input to understand the underlying mechanisms of failure with focus on SFGs. This is of fundamental interest for the design of future mechanical sensors incorporating piezoresistive single-walled CNTs as the sensing element.