This paper reports the preparation of microgels with an interpenetrating polymer network (IPN) structure using microfluidic synthesis. Microgels with a narrow size distribution were generated from ionically cross-linked alginate and chemically cross-linked poly(N-isopropylacrylamide). The mechanical properties of the microgels, such as Young's modulus and the characteristic relaxation time, were studied using atomic force microscopy (AFM). The lower limits of the elasticity found in this study are within the range of the elasticity reported for neutrophils, making these microgels a promising model system for studies of cell flow through constrained geometries.