A swage or coupling tool is provided for use in coupling a fluid line to a compression fitting, a fluid coupler, or the like. The swage tool provides multiple degrees of freedom and/or multiple pivots or pivot joints to facilitate and maintain alignment of the jaws with the compression fitting during use of the swage tool to facilitate properly-aligned assembly of the compression fitting, and to limit bending or kinking of the fluid line when the fitting is being attached. The swage tool includes a pair of movable jaws, which may have stepped or rounded engagement surfaces, which may be forced against corresponding engagement surfaces of the compression fitting to securely assemble the fitting to the fluid line. The shape of the engagement surfaces facilitates properly-aligned assembly of the compression fitting, and limits bending or kinking of the fluid line when the fitting is being attached.