Prepare the artichokes by trimming the stems. Peel away any browned or dry outer leaves. Chop off the tops of the artichokes (about one inch of the way down). Rub the cut edges of the artichokes with the cut half of the lemon to prevent the leaves from browning.
Pour 1 cup of water into the Instant Pot. Place the metal steam rack/trivet or steamer basket inside. Set the artichokes upright on the rack, stacking them if necessary. Place the lid on and turn the steam release valve to Sealing. Press the Pressure Cook or Manual button and set the cook time to 10 minutes.
When the Instant Pot beeps, let the pressure release naturally for 10 minutes, then carefully switch the steam release valve to Venting.
Meanwhile, gently melt the butter in a small saucepan over medium heat, stir in the grated garlic and salt, and simmer for 1 minute. Remove the garlic butter from the heat.
When the pressure is fully released, open the lid. Use tongs to carefully remove the artichokes to serving plates. Serve the artichokes with lemon wedges and individual dishes of melted garlic butter for dipping.