Sivir's Boomerang Blade returns to her after reaching the max range, so you can shift position to hit enemies who would otherwise have evaded it.
Ricochet resets Sivir's basic attack timer on activation, so activating this immediately after landing a normal basic attack will maximize damage output.
Try saving Spell Shield for enemy abilities that can disable you such as stuns and roots.
Boomerang Blade costs a lot of mana to cast, so dodging it sets Sivir back. If it hits you on the way out, avoid its path on the way back.
Sivir is a powerful pushing champion, so leaving her unattended in a lane for too long will often result in your turrets being destroyed.
When laning against Sivir, it is possible to throw off the timing of her Spell Shield by faking an advance, then backing off.