Enigmatic rhymes with:
dogmatic, phlegmatic, pragmatic, aromatic, asthmatic, asymptomatic, automatic, axiomatic, charismatic, cinematic, climatic, diagrammatic, diplomatic, dogmatic, dramatic, emblematic, enzymatic, epigrammatic, idiomatic, informatic, klezmatic, mathematic, matic, mattick, melodramatic, monochromatic, numismatic, phlegmatic, pneumatic, posttraumatic, pragmatic, prismatic, problematic, programmatic, psychosomatic, rheumatic, schematic, semiautomatic, sensormatic, symptomatic, systematic, telematic, thematic, traumatic, undiplomatic
Enigmatic sounds like:
engagements, enhancements, enjoyments, enzymatic