We fabricate a series of reconfigurable waveguide interferometers using laser machining techniques and charac- terize them classically. The 3D nature of the ultrafast laser writing technique allows for the fabrication of unique multi-arm interferometers not possible in planar platforms. We demonstrate selectivity between multiple phase shifters in a single interferometer by patterning the chip surface using picosecond laser ablation in a separate step. Microfluidic elements for making practical measurements on-chip are incorporated by machining channels within the substrate to interact with waveguide modes. Our results provide a path toward practical implementation of quantum metrology protocols requiring multiple interferometer arms and tunable phases.