Carbon nanomaterials have received increased attention in the last few years due to their potential applications in several areas. In medicine, for example, these nanomaterials could be used as contrast agents, drug transporters, and tissue regenerators or in gene therapy. This makes it necessary to know the behavior of carbon nanomaterials in biological media to assure good fluidity and the absence of deleterious effects on human health. In this work, the rheological characterization of different graphene nanomaterials in fetal bovine serum and other fluids, such as bovine serum albumin and water, is studied using rotational and microfluidic chip rheometry. Graphene oxide, graphene nanoplatelets, and expanded graphene oxide at concentrations between 1 and 3 mg/mL and temperatures in the 25–40 °C range were used. The suspensions were also characterized by transmission and scanning electron microscopy and atomic force microscopy, and the results show a high tendency to aggregation and reveals that there is a protein–nanomaterial interaction. Although rotational rheometry is customarily used, it cannot provide reliable measurements in low viscosity samples, showing an apparent shear thickening, whereas capillary viscometers need transparent samples; therefore, microfluidic technology appears to be a suitable method to measure low viscosity, non-transparent Newtonian fluids, as it is able to determine small variations in viscosity. No significant changes in viscosity are found within the solid concentration range studied but it decreases between 1.1 and 0.6 mPa·s when the temperature raises from 25 to 40 °C.