Assisted reproductive technology (ART) can benefit from the features of microfluidic technologies, such as the automation of time-consuming labor-intensive procedures, the possibility to mimic in vivo environments, and the miniaturization of the required equipment. To date, most of the proposed approaches are based on polydimethylsiloxane (PDMS) as platform substrate material due to its widespread use in academia, despite certain disadvantages, such as the elevated cost of mass production. Herein, we present a rapid fabrication process for a cyclic olefin copolymer (COC) monolithic microfluidic device combining hot embossing—using a low-temperature cofired ceramic (LTCC) master—and micromilling. The microfluidic device was suitable for trapping and maturation of bovine oocytes, which were further studied to determine their ability to be fertilized. Furthermore, another COC microfluidic device was fabricated to store sperm and assess its quality parameters over time. The study herein presented demonstrates a good biocompatibility of the COC when working with gametes, and it exhibits certain advantages, such as the nonabsorption of small molecules, gas impermeability, and low fabrication costs, all at the prototyping and mass production scale, thus taking a step further toward fully automated microfluidic devices in ART.