Measure the width & thickness of your engagement ring band/shank and pair with bands that are the same or slightly thinner so as to "blend in" without looking too thin in comparison.
For example, a 2mm thick engagement ring will go best with a 1.6mm - 2.0mm band. Or a 1.5mm thick engagement ring with a 1.2mm - 1.5mm thick band (same general rule goes for the width).
Also note the shape of your engagement band/shank... round / flat square / rectangular with rounded edges / etc in order to intentionally match OR contrast the band shape.
Also measure the space available beneath the center stone area, is there enough space for a band in the thickness you're looking for? If there is no space underneath, open cuff rings are a great option.
Please send any questions to info@KARAT1424.com