Here's a purely-devil's-advocate alternate reading of the effect of twin-spelling a booming blade:
"As part of the action used to cast this spell, you must make a melee attack with a weapon against one creature within the spell’s range, otherwise the spell fails."
Okay; so we attack one creature with our melee weapon when we cast this spell. It is not directly stated that the creature we attack with our melee weapon needs to be the target of the spell, but I presume this is implied. If, for whatever reason, we can't take the attack, then the spell fails. If we can and we miss, the target (of the spell) suffers no effect. However, ...
"On a hit, the target suffers the attack’s normal effects, and it becomes sheathed in booming energy until the start of your next turn."
This seems to outline the effect of the spell on the target. The result of the spell is to cause the target (of the spell) to "suffer the attack's normal effect, and ...."
When you use twin spell, you get to "target a second creature in range with the same spell."
Putting that together, the ideal-nit-picky-rules-legal procedure seems to be as follows:
Cast the twin spell, simultaneously attacking
one creature with your sword (or whatever). If the attack hits, the
two targets (of the
spell) will "suffer the attack's normal effect," (which includes the weapon damage and, at higher levels, the bonus d8s of thunder damage), and
both targets (of the spell) will become "sheathed in booming energy until the start of your next turn."
This reading clearly separates the cost of "make a melee attack" from the effect of "suffer the attack's normal effect and [stuff with thunder and whatnot]."
I think it addresses the gold coin counterexample that
@lumenbeing brought up. Imagine that the effect of the hypothetical "toss a gold coin" spell (let's call it ... "Leprechaun's Luck") is that the target gains a luck point (as the Lucky feat). Twinning this hypothetical spell would still only involve tossing one gold coin to one creature (similar to the one attack roll of Booming Blade), but two people would gain the luck point (similar to the weapon and thunder damage/effect of Booming Blade).
It also addresses
@TheKing in not giving another attack roll. Indeed, only one attack roll is used. The other target just unluckily suffers an effect of a spell.
As I mentioned, this is a purely-devil's-advocate reading. How I would play or DM it would be in the "natural" reading of twinned spell --> two melee attacks, resolved individually (like
@Esker and others mentioned).