A strategic modification of acidity (pK a values) by the non-covalent host-guest interactions is one of the most promising concepts in current supramolecular chemistry. This work is aimed at enhancing the effectiveness of capillary electrophoresis (CE) in determination of pK a shifts caused by such interactions and their thermal dependencies crucial in a deep thermodynamic description. We show how to (i) minimize the systematic errors related to Joule heating, (ii) minimize the influence of a voltage ramp time, (iii) speed up pK a shift identification and estimation, (iv) interpret thermal effects related to two overlapped dynamic equilibria, and (v) determine pK a shifts by an alternative spectrophotometric method (CE-DAD). The proposed solutions were implemented to examine the supramolecular pK a shifts of several coumarin derivatives, caused by a variety of structurally different cyclodextrins. It was revealed that a specific host substitution pattern determines the magnitude of apparent pK a shifts. Accordingly, heptakis(2,6-di-O-methyl)-β-cyclodextrin induces the much stronger shifts than both non-methylated-β-cyclodextrin and heptakis(2,3,6-tri-O-methyl)-β-cyclodextrin applied at the same concentration. We also show that insofar as the complexation of 4-hydroxycoumarin and its derivative (coumatetralyl) are similarly exothermic, the thermal effects accompanying the deprotonation process are remarkably different for both molecules. The pK a shift induced by complexation with calixarene was also for the first time determined by a CE method. These observations throw a new light on the background of acidity modification and confirm the applicability of CE as an analytical tool.