I have asthma and riding up steep hills can be a trigger for me. I've found it best to slow my cadence way down while riding in the lowest gear on my bike. I routinely slow to ~3 mph when climbing steep hills. Haven't fallen yet. Just keep pedaling.

I recently did a big club ride, a metric century, that had a steep hill near the end. I rode the entire route with a 70-year-old who rides almost every day including long rides on weekends (Saturday AND Sunday). He rides a touring bike, definitely not what most would consider ideal for climbing. He and I slowly pedaled up the hill. It wasn't easy but neither of us was ever in doubt that we would make it. At the end of the ride we learned that some of the A-level riders had walked up that hill. Tortoises > hares.