The EphB2 receptor is known to be overexpressed in various types of cancer and is therefore a promising target for tumor cell imaging by positron emission tomography (PET). In this regard, imaging could facilitate the early detection of EphB2-overexpressing tumors, monitoring responses to therapy directed toward EphB2, and thus improvement in patient outcomes. We report the synthesis and evaluation of several fluorine-18-labeled peptides containing the SNEW amino acid motif, with high affinity for the EphB2 receptor, for their potential as radiotracers in the non-invasive imaging of cancer using PET. For the purposes of radiofluorination, EphB2-antagonistic SNEW peptides were varied at the C terminus by the introduction of L-cysteine, and further by alkyne- or azide-modified amino acids. In addition, two novel bifunctional and bioorthogonal labeling building blocks [18F]AFP and [18F]BFP were applied, and their capacity to introduce fluorine-18 was compared with that of the established building block [18F]FBAM. Copper-assisted Huisgen 1,3-dipolar cycloaddition, which belongs to the set of bioorthogonal click chemistry reactions, was used to introduce both novel building blocks into azide- or alkyne-modified SNEW peptides under mild conditions. Finally, the depletion of copper immediately after radiolabeling is a highly important step of this novel methodology.