Phase shifters are a key component of nulling interferometry, one of the potential routes to enabling the measurement of faint exoplanet spectra. Here, three different achromatic phase shifters are evaluated experimentally in the mid-infrared, where such nulling interferometers may someday operate. The methods evaluated include the use of dispersive glasses, a through-focus field inversion, and field reversals on reflection from antisymmetric flat-mirror periscopes. All three approaches yielded deep, broadband, mid-infrared nulls, but the deepest broadband nulls were obtained with the periscope architecture. In the periscope system, average null depths of 4x10(-5) were obtained with a 25% bandwidth, and 2x10(-5) with a 20% bandwidth, at a central wavelength of 9.5 mum. The best short term nulls at 20% bandwidth were approximately 9x10(-6), in line with error budget predictions and the limits of the current generation of hardware.