Evenhandedly rhymes with:
candidly, handedly, mindedly, singlehandedly, candidly, guardedly, handedly, mindedly, singlehandedly, admittedly, assertedly, candidly, discontentedly, good-heartedly, guardedly, handedly, heartedly, heatedly, mindedly, placidly, pointedly, purportedly, repeatedly, reputedly, rigidly, singlehandedly, unabashedly, undoubtedly, unexpectedly, unprecedentedly, validly, wholeheartedly, wickedly, wretchedly
Evenhandedly sounds like:
evendale, eventual, eventually