Preheat the oven to 400ºF. Slice off any dry or woody ends from the asparagus spears (usually about the bottom inch or so).
Spread the asparagus spears out over half of a large baking sheet. Add the grape tomatoes to the other half. Drizzle 1 Tbsp olive oil over each side. Toss the vegetables to coat in the oil.
Add the minced garlic to the tomatoes and toss to combine. Add a generous pinch of salt and pepper to each of the vegetables.
Roast the vegetables for 20 minutes, then give them a stir. Return the vegetables to the oven and roast for another 10 minutes. Stir again, then continue to roast, checking every five minutes, until the vegetables have reached your desired level of doneness (35 minutes total roasting time for me). If one vegetable finishes before the other, simply remove it from the baking sheet and finish roasting the other.
After roasting, taste the vegetables and season one last time with a pinch of salt and pepper.