Using photometry collected with the Zwicky Transient Facility, we are conducting an ongoing survey for binary systems with short orbital periods ( ${P}_{{\rm{b}}}\lt 1\,\mathrm{hr})$ with the goal of identifying new gravitational-wave sources detectable by the upcoming Laser Interferometer Space Antenna (LISA). We present a sample of 15 binary systems discovered thus far, with orbital periods ranging from 6.91 to 56.35 minutes. Of the 15 systems, seven are eclipsing systems that do not show signs of significant mass transfer. Additionally, we have discovered two AM Canum Venaticorum systems and six systems exhibiting primarily ellipsoidal variations in their lightcurves. We present follow-up spectroscopy and high-speed photometry confirming the nature of these systems, estimates of their LISA signal-to-noise ratios, and a discussion of their physical characteristics.