We present a deep neural network-based framework for designing multi-band microstrip antennas given a desired impedance matching spectrum. The approach enables a design methodology that generates the desired antenna structures rapidly (under a second) through an effective deep learning- enabled search of a large design space and eliminates the need for extensive domain knowledge of antenna design. The framework is built on our innovations in tandem neural networks consisting of two cascaded neural networks. Our structures are parameterized in an exponentially large design space of discrete variables (pixels), leading to the realization of nonintuitive structures. This end-to-end synthesis in terms of discrete variables is enabled by introducing a new type of “smooth thresholding” activation function, which, along with crucial regularization terms in the network loss function, aids in designing our structures. We perform extensive neural network optimizations and study various trade-offs in the design process. We demonstrate the efficacy of our methods by generating single and dual-band resonant structures, which can be up to 50% more compact in terms of area, and up to 18 % thinner in terms of substrate height than conventional structures, while retaining competitive performance parameters in terms of gain, polarization properties, radiation efficiency, and fractional bandwidth.