I recently had a situation come up where an NPC was using Booming Blade against the players. They came up with some creative ways to get out of the damage triggered by movement and I was wondering if there's any official ruling on how this should work.

One of the player characters used Misty Step to teleport away and then use their regular movement. Another player character used an explosion effect to "forcibly" move themselves without triggering the damage. Do teleportation and/or forced movement disable the Booming Blade damage triggered by movement?

There's nothing in the spell saying that the effect ends if the target uses other means of movement, so I thought the effect would still be in place and trigger whenever they take willing movement. Is there any official ruling on this?

This is one of those grey areas that depends on the interpretation of the mechanics of teleportation.

I would rule that teleportation or forced movement + subsequent voluntary movement would trigger, but teleportation alone would not. The only reason that forced movement doesn't trigger the effect is spell balance. It's meant to be a control+damage spell, not an exploit to get double damage at will.

Forced movement shouldn't, teleportation might depending on DM interpretation, but regardless additional movement after still will. The effect didn't end because they found a way to move without moving, the effect lasts until the caster' s next turn starts.

While you effectively move when using teleportation, It more depends if the DM interpret the distance teleported as willingly moving 5 feet+ or not. 

To move while prone, you must crawl or use magic such as teleportation.

According to the Devs Booming Blade  refers to movement in normal sense though;

@DnDAthenaeum In SCAG, under Booming Blade, does movement refer only to overland movement, or any movement (like an attack, waving, etc.)

@JeremyECrawford When booming blade refers to moving, it means movement in the game's normal sense: moving X feet.

My read on this is that the teleportation would not activate the booming blade movement effect, but it would also not free the target from being sheathed in booming energy for the duration.

If I were DMing, my ruling would be that teleporting would not trigger the extra damage; however since the effect is tied to them and not an area, any subsequent movement after the teleport would still trigger the extra damage. As for the forced movement, booming blade specifically states willingly moving and while trigger the forced movement yourself might be willful it is not through your own muscles so it wouldn't trigger it; however like with the teleportation any movement after the forced movement would still trigger booming blade