Plasmids play a vital role in synthetic biology by enabling the introduction and expression of foreign genes in various organisms, thereby facilitating the construction of biological circuits and pathways within and between cell populations. For many applications, maintaining functional plasmids without antibiotic selection is critical. This study introduces an open-hardware-based microfluidic workflow for analyzing plasmid retention by culturing single cells in gel microdroplets and quantifying microcolonies using fluorescence microscopy. This approach allows for the parallel analysis of numerous droplets and microcolonies, providing greater statistical power compared to traditional plate counting and enabling the integration of the assay into other droplet microfluidic workflows. By using plasmids expressing fluorescent proteins alongside a non-specific fluorescent DNA stain, single colonies can be identified and differentiated based on plasmid loss or fluorescent marker expression. Notably, this advanced workflow, implemented with open-source hardware, offers precise flow control and temperature management of both the sample and the microfluidic chip. These features enhance the workflow's ease of use, robustness, and accessibility. While the study focuses on Escherichia coli as the experimental model, the method's true potential lies in its versatility. It can be adapted for various studies requiring fluorescence signal quantification from plasmids or stains, as well as for other applications. The adoption of open-source hardware broadens the potential for conducting high-throughput bioanalyses using accessible technology in diverse research settings.