Prepare the artichokes by trimming the stems flush with the bottoms. Peel away any browned outer leaves. Chop off the tops of the artichokes (about one-quarter of the way down). Using kitchen shears, snip off the thorny tips of the remaining leaves. Rinse the artichokes under running water and shake off excess water. Rub the cut edges of the artichokes with the cut half of the lemon to help slow them from browning.
Pour the 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. Secure the lid 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, allow the pressure to release naturally for 10 minutes, then carefully switch the steam release valve to Venting.
Meanwhile, if using the already-made compound butter, melt it in a small saucepan over low heat. If making fresh garlic butter, gently melt the butter in a small saucepan over medium heat, stir in the grated garlic, and simmer for 1 minute. Remove either 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.
“Medium” artichokes weigh about 1/4 pound and are approximately the size of softballs. If you are using larger artichokes, you will need to adjust the cooking time accordingly. Start by adding 3 to 5 minutes of cooking time. You can always reseal the Instant Pot and add more time if needed.