I need to run a dedicated 220V line to a new Advantium microwave oven in a kitchen remodel. I have an existing 220V line that went to an electric cooktop that was replaced with a gas cooktop. Can I splice into the existing 220V line that did run to the old cooktop and extend that line in the crawl space under the floor a distance of approximately 12 feet to the new oven's location? Thank you.

Sure, just use the same size wire, be sure the breaker matches the circuit the microwave needs, splice the two cables in a junction box with wirenuts and cover the box. Leaving the box mounted under the cabinet will be fine, as long as the box does not get buried in the wall.