I already wrote a post on how to embed Soundcloud content so why not to do the same for Bandcamp?
If Soundcloud is more like a sharing platform for musicians, radio stations, podcasters, etc, Bandcamp is more intended to preview and sell digital music (but you can also buy CDs and LPs).
This means that is more likely to find entire albums uploaded by the label itself that can be entirely previewed with decent quality mp3s (128 kbps).
Alright then head to Bandcamp.com as start looking for your favorite artist, once you find something that you want to share click the Share / Embed button under the Album/Song artwork then click on Embed this album
Then select a frame (you can change it later by modifying the Layouts option)
At this point you can modify the frame, colors and size as you wish. Notice that only one is useful when embedding an entire album, be sure to check Show tracklist. You can also output WordPress specific code with ease