In illustrative implementations of this invention, microfluidic perfusion tubing is easily and precisely inserted into a microfluidic device. The tubing is inserted in a manner that aligns one or more holes in the perfusion tubing with one or more channels in the microfluidic device. For example, a hole in the tip of a perfusion tube may open into a channel in the microfluidic device. Or, multiple holes in a tube may open into different channels in a microfluidic device. The system may include a microfluidic device, two or more couplers, and a support frame. The microfluidic device may be inserted into a recessed region of the support frame, and the couplers may be attached to the support frame. The effect of doing so is to fix the position of the components relative to each other, and to precisely align holes in the tubes with channels in the microfluidic device.