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In the study of micro-swimmers, both artificial and biological ones, many-query problems arise naturally. Even with the use of advanced high performance computing (HPC), it is not possible to solve this kind of problems in an acceptable amount of time. Various approximations of the Stokes equation have been considered in the past to ease such computational efforts but they introduce non-negligible errors that can easily make the solution of the problem inaccurate and unreliable. Reduced order modeling solves this issue by taking advantage of a proper subdivision between a computationally expensive offline phase and a fast and efficient online stage. This work presents the coupling of Boundary Element Method (BEM) and Reduced Basis (RB) Reduced Order Modeling (ROM) in two models of practical interest, obtaining accurate and reliable solutions to different many-query problems. Comparisons of standard reduced order modeling approaches in different simulation settings and a comparison to typical approximations to Stokes equations are also shown. Different couplings between a solver based on a HPC boundary element method for micro-motility problems and reduced order models are presented in detail. The methodology is tested on two different models: a robotic-bacterium-like and an Eukaryotic-like swimmer, and in each case two resolution strategies for the swimming problem, the split and monolithic one, are used as starting points for the ROM. An efficient and accurate reconstruction of the performance of interest is achieved in both cases proving the effectiveness of our strategy.