A little more information would be useful in giving you information. What specifically do you mean by medium and high. What seasons are you contemplating? Specific peaks??
There is a big difference between an icy couloir in the summer and the same terrain in winter and different boots for those conditions are essential.
Today, most crampons are adjustable and can fit wide variety of boots.
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Hi @Andres93 - It’s exciting to hear you have some adventures lined up requiring crampons! We have lots of different options of crampon-compatible boots, so it’s best to have some more info before we suggest any specific brands and models of boots.
Do you already have crampons and are looking for boots that will work with them? If not, we have a great Expert Advice article on picking crampons. And, as @hikermor asked, where are you headed? Knowing the destination/terrain will help with recommendations. In general, true mountaineering boots allow you to use hybrid or step-in crampons, while hiking/backpacking boots work with strap-on crampons. With hiking/backpacking boots, you are usually looking for a stiff sole and a lip on the back of the boot.
And final thought - finding the right boot can be tricky online, so we always recommend either visiting an REI store or setting up a free virtual outfitting appointment to make sure you have the ideal set-up.
Hope this is a good start. Good luck with your trip!
I have a very short crampon story. When I was climbing the Matterhorn, I had crampons on my Koflach plastic boots for mixed sections.
I was on a very steep vertical rock pitch when the crampon on my right boot came off! Fortunately, the upper strap held and it just dangled there until I was able to re-attach it as soon as I reached a safe 'platform'.
The summit/near summit ice fields were especially sketch, so I made sure they were clamped on tight!
end of story.