I carry a small hand pump ,no not a bicycle pump but a 1/2 size regular pump it fits in my panniers with my tyre repair stuff, strings, pressure pack tyre repair plugs ect, and have repaired a few punctures over the years, using various methods ,but a good supply of air means you can have a few goes at the repair or limp home stopping as required
one failure that will leave you stranded is a split valve stem, a real PITA to replace on the side of the road ,it pays to replace these every time you get a new tyre for the small cost involved they do deteriorate, good tyre places do it routinely without being asked,