Paste-up pairs mainly occur on flat plate printed coil stamps. What follows here is a general description of what they are and how often they occur. The details may vary for some specific stamp issues.
Flat plate coil stamps were printed on sheets of paper using printing plates that were 400 subjects in size (20 by 20 stamps). The longest strip that could be obtained was 20 stamps long. To create coil rolls that had 100, 500, etc stamps per roll, an operator had to splice together the smaller strips of 20 stamps to form the size needed. For example, a coil roll of 100 stamps required 5 strips of stamps resulting in 4 paste-up pairs on one roll.
Paste-up pairs are easily noticeable from the back of the stamp. The double thick paper is a dead give away. A strip of stamps had selvedge (called a tab) which was affixed to the back of the other strip of stamps. Sometimes, the plate number or other plate markings were left over on the selvedge and they are part of the paste-up pair.
Paste-up pairs are usually not very well centered. Operators were concerned about getting the strips attached. Lining them up perfectly was not a major concern. Tiny misalignments are common. And because the stamps were cut apart before splicing, one stamp may have (for example) very fine centering while the other stamp may only have fine centering. Paste-up pairs where both stamps have very fine centering are much more scarce.
You’re probably thinking, why not just leave the strips loose and roll them into a roll of 100 or more? Stamp vendors had special equipment for dispensing stamps. Some companies making large mailings had specialized equipment that would both dispense and affix a coil stamp to a letter. Large coil rolls alleviated the need for someone to constantly refill the stamp dispensing and affixing machines.
What are paste-up pairs worth? The Scott catalog lists prices for paste-up pairs for most flat plate issues. Paste-up pairs showing other marginal markings such as plate numbers are worth a premium. Some plate numbers are only known on paste-up pairs.
The introduction of rotary press stamps almost eliminated the need for paste-up pairs. Instead of stamps being printed by the sheet, stamps were now printed continuously from large rolls of paper. Large quantities of stamps could be printed from a single roll. Rolls of coils were continuous. The only time a paste-up pair was created was when there was a tear in the roll of paper and the printing press operator had to splice the web of paper back together. Or when the roll of paper ran out and the next roll of paper was attached to the end to keep the continuous feed of paper going. Either way, the occurrences of paste-up pairs on rotary press printed stamps are much rarer and not listed in the Scott catalog. Paste-up pairs on rotary press stamps are considered freaks or oddities since they were not normally produced and usually disposed of during the printing process.