Measuring the size of micron-scale particles plays a central role in the biological sciences and in a wide range of industrial processes. A variety of size parameters, such as particle diameter, volume, and mass, can be measured using electrical and optical techniques. Suspended microchannel resonators (SMRs) are microfluidic devices that directly measure particle mass by detecting a shift in resonance frequency as particles flow through a resonating microcantilever beam. While these devices offer high precision for sizing particles by mass, throughput is fundamentally limited by the small dimensions of the resonator and the limited bandwidth with which changes in resonance frequency can be tracked. Here, we introduce two complementary technical advancements that vastly increase the throughput of SMRs. First, we describe a deconvolution-based approach for extracting mass measurements from resonance frequency data, which allows an SMR to accurately measure a particle's mass approximately 16-fold faster than previously possible, increasing throughput from 120 particles/min to 2000 particles/min for our devices. Second, we describe the design and operation of new devices containing up to 16 SMRs connected fluidically in parallel and operated simultaneously on the same chip, increasing throughput to approximately 6800 particles/min without significantly degrading precision. Finally, we estimate that future systems designed to combine both of these techniques could increase throughput by nearly 200-fold compared to previously described SMR devices, with throughput potentially as high as 24 000 particles/min. We envision that increasing the throughput of SMRs will broaden the range of applications for which mass-based particle sizing can be employed.