As dividing cells transition into mitosis, hundreds of proteins are phosphorylated by a complex of cyclin-dependent kinase 1 (CDK1) and Cyclin-B, often at multiple sites. CDK1:Cyclin-B phosphorylation patterns alter conformations, interaction partners, and enzymatic activities of target proteins and need to be recapitulated in vitro for the structural and functional characterization of the mitotic protein machinery. This requires a pure and active recombinant kinase complex. The kinase activity of CDK1 critically depends on the phosphorylation of a Threonine residue in its activation loop by a CDK1-activating kinase (CAK). We developed protocols to activate CDK1:Cyclin-B either in vitro with purified CAKs or in insect cells through CDK-CAK co-expression. To boost kinase processivity, we reconstituted a ternary complex consisting of CDK1, Cyclin-B, and CKS1. In this work, we provide and compare detailed protocols to obtain and use highly active CDK1:Cyclin-B (CC) and CDK1:Cyclin-B:CKS1 (CCC).