There's a whole interesting set of laminators designed for use with very small items: business cards, tags, Ids, trinkets for kids. Some are portable, some are handle-driven, some are hot, some are cold. Following is a description of some of them, to indicate the applications and the use of the machines.
The Universal 84526 is small: portable, electrically operated or manual, 15.l" x 5.5" x 3.25, 6.1 lbs; pouch laminator, accepts up to 8.5" x 14" papers. The 84528 model is similarly powered; it is a very small unit, with a maximum width of 4". It's poky: 7.75" x 9.5" x 4.25": also a pouch laminator. It's worth shopping around for these units: they are inexpensive to begin with but some places are more inexpensive than others.
Fellowes has a romantically named series of light, slow, low-volume laminators: Saturn, Mars, Venus, Jupiter, Cosmic, and the boring EXL. The EXL is a 4" photo-laminator: the others are small (maximum 16" wide) and light, suitable for home and general low-volume use; they all look rather crouchy. They vary in sophistication and controls.
The ubiquitous GBC makes a Quartet of compact machines. These do pouch lamination up to 12" and at least one does cards as well. They are all small to very small except for the Ultima 35 which about the same size as an ordinary cash register.
The Oasys OLA6 & OLA7 systems produce ISO-quality standard laminated cards. They are quite large desktop machines. The cards to be laminated are placed in a feed tray which is inserted into the machine: the act of insertion starts the process which continues until the whole batch is processed and has cooled down, at which point the tray is released. There are actually two input slots so one tray can be loaded while the other is processed. There are tow small machines for punching cards available along with a flex-tester, which twists the cards to make sure they meet ISO standards.
There are a great many more manufacturers for these small machines; Xyron is of course one of them.
(There is at least one "compact" laminator that doesn't belong in this section. That's the Emseal Compact series: they are all hot-roll machines handling widths from 14" to 40").