Natural clinoptilolite was studied to assess its performance in removing caesium and strontium ions, using both static columns and an agitated tube reactor (ATR) for process intensification. Kinetic breakthrough curves were fitted using the Thomas and Modified Dose Response (MDR) models. In the static columns, the clinoptilolite adsorption capacity (qe) for 200 ppm ion concentrations was found to be ~171 and 16 mg/g for caesium and strontium, respectively, highlighting the poor material ability to exchange strontium. Reducing the concentration of strontium to 100 ppm, however, led to a higher strontium qe of ~48 mg/g (close to the maximum adsorption capacity). Conversely, halving the column residence time to 15 min decreased the qe for 100 ppm strontium solutions to 13–14 mg/g. All the kinetic breakthrough data correlated well with the maximum adsorption capacities found in previous batch studies, where, in particular, the influence of concentration on the slow uptake kinetics of strontium was evidenced. For the ATR studies, two column lengths were investigated (of 25 and 34 cm) with the clinoptilolite embedded directly into the agitator bar. The 34 cm-length system significantly outperformed the static vertical columns, where the adsorption capacity and breakthrough time were enhanced by ~30%, which was assumed to be due to the heightened kinetics from shear mixing. Critically, the increase in performance was achieved with a relative process flow rate over twice that of the static columns.