Structure-property relationships in various 12- and IS-layer hexagonal perovskites have been investigated for use in Microwave Dielectric (MD) applications. Specifically; (i) the structural origin(s) of a peak in Er at 465 K for the 12-layer hexagonal perovskite Ba3LaNb3012, BLN, and its effect on the Temperature Coefficient of resonant Frequency, TCF; (ii) synthesis and structure-property relationships of related 12-layer hexagonal perovskites based on Ba3RENb)012 and Sr)RENbJOI2 with RE ions smaller than La3+ ; (iii) a study of the IS-layer hexagonal perovskite solid solution phase (Bas-xSrx)Nb4015 to establish if similar properties to BLN can be obtained and therefore improve our understanding of how octahedral tilting in hexagonal perovskites influences their microwave dielectric properties. (i) A study of the BLN crystal structure using mode analysis of Neutron Powder Diffraction, NPD data showed the structure to go from one with a tilted NbOIi network (space group RI) at 300 K to un-tilted (space group RIm) at 500 K. On cooling, the change in Nb06 framework at - 500 K causes displacement of the A-site cations from their ideal positions within the AO .• layers at - 465 K; it is this movement of A-site cations in response to octahedral tilting that gives rise to the peak in Er. Raman Spectroscopy, RS showed the loss of a peak (- 425 cm -I) at - 400 K that is associated with the phase transition. (ii) Ba,RENbJOl2 with RE = Pr3+ or Nd3+ did not exhibit resonance at microwave frequencies. Instead a relaxor-type response was observed from radio frequency measurements with a maximum in I::r near or below room temperature. NPD and RS data showed this behaviour is linked to size mismatch (cation variance) between the A-site cations. Sr3PrNb3012 showed encouraging microwave dielectric properties with I::r - 35, Q.f - 17,000 GHz and TCF - 8 ppm K-'. (iii) The (Bas_xSrx)Nb4015 study found materials that do show similar properties to BLN. Sr-rich members of this study vi can be described has having a tilted NbOf, network (space group PJe!) whereas the Ba- rich members contain untilted Nb06 octahedra (space group PJmJ) at room temperature. This change from a tilted to untilted structure as the Ba content increases leads to a crossover from a tilt to untilt system at room temperature for Ba2:;Sr2.sNb4015 (B2.5S2SNO). This crossover at B2.5S2.sNO is reflected in the room temperature er and TCF (Er - 47, TCF - 343 ppm K-1) which have their highest values for this composition. This provides confirmation of the effect octahedral tilting can have on MD properties. The trend in Q.f is obscured by extrinsic effects, for example as a result of an irregular ceramic microstructure (SrsNb40ls) and the presence of impurities that exist as intergrowths within the main phase. The analysis of the FWHM of M" Debye peaks from IS data was useful to detect electrical heterogeneity within the grains and could be used to link with Q.f. vii