You tried too hard too early trying to keep up.
The big secret is knowing to stop early or to take it easy early. I learned this lesson via my HRM - see, the stupid things are good for something after all. In the early days of my return to cycling, I stubbornly stuck to the 'keep going, keep going' mentality - a nice bit of bravdo when you're young but seriously counter productive for us old blokes. Once I got the HRM, I noticed it'd zoom up to something approaching my max and that'd be it. I'd push and push until I just had to stop, then recover. At some point, I decided this was too hard and started stopping a bit earlier. Whereas before I'd push my HR to over 180 before stopping (scarily close to my observed max of 185), I now pushed it to 170 before stopping. I used to wait until my HR was 130 before moving off again. With that earlier stop, I found that even though I rested the same, that second stint lasted a lot longer and I was a lot stronger than if I went that bit further. By not going so hard (ie, pushing myself further), I actually had fewer stops. Of course, after a few months, I was riding those hills without stopping at all. Hell, nowadays, my MR doesn't even go over 165 climbing up Flagstaff Hill (my regular big hill) whereas at one time, it was a three stop hill. I'm at the point now where I could pull higher gears, but probably wouldn't be able to maintain the same cadence ... so I'm sticking with my granny for a bit longer.
The secret (for me), is to settle on a good cadence of 90-95 before hitting the steep bit of the climb - easy on Flagstaff because you've actually been climbing for well over a km before you hit the hill itself. Then work the gears down (pretty quickly as I hit the hill) until I can't go any lower and then sit on that cadence. I keep that cadence going even when the hill flattens - just go up a gear or two or three, then work down again it increases.
If I try to go too hard too early (eg, pushing too high a gear in an attempt to keep the speed up), I die and can't recover quickly, which is what you experienced. By starting easy, setting the rhythm and maintaining it using the gears, I find I get to the top of hills still generating power and it's not unknown for me to come over the crest of Flagstaff on the big ring and doing 30km/hr (it flattens out in the last couple of hundred metres to the top).
As the slope of the hill varys, I choose the gear that gives me the same cadence with the same perceived effort ie, I don't spin out but don't go pushing hard on the pedals either. Nor do I stand because that spikes the HR - I stand only when I know I'm about to hit a crest and will have an opportunity to recover. On a climb that was going to take half an hour or more, I might stand to ease the old rump.
That's the fat old git's guide to getting up stupid hills he should have enough sense to avoid.
Richard