Semi-directed networks provide a graphical structure for describing the evolutionary history of organisms in the presence of hybridization. We introduce two algorithms for reconstructing semi-directed level-1 phylogenetic networks from their complete set of 4-leaf subnetworks, known as quarnets. The sequential algorithm begins with a single quarnet and adds one leaf at a time until the entire network has been reconstructed. The cherry-blob algorithm is a novel approach inspired by cherry-picking techniques on trees