A dielectric ceramic composition is disclosed which includes: a main ceramic composition of barium oxide and titanium oxide, or barium oxide, titanium oxide and at least one of strontium oxide, calcium oxide, zirconia and zinc oxide, which composition is represented by (1-a-b)BaO.aSrO.bCaO.x[(1-c)TiO.sub.2.cZrO.sub.2 ].yZnO, where 3.1.ltoreq.x.ltoreq.5.4, 0.ltoreq.y.ltoreq.2.9, 0.ltoreq.a+b.ltoreq.0.4, 0.ltoreq.c.ltoreq.0.2; and a secondary component at least a part of which consists of a B.sub.2 O.sub.3 material or a glass material containing B.sub.2 O.sub.3 as one of glass components, the secondary component being added to the main ceramic composition, in an amount of 0.1-7.5 parts by weight of B.sub.2 O.sub.3 per 100 parts by weight of the main ceramic composition. Also disclosed are a method of preparing such a dielectric ceramic composition, a dielectric resonator for microwave application which uses the dielectric ceramic composition, or a dielectric filter having a plurality of such dielectric resonators, and a method of producing the dielectric resonator or dielectric filter.