Grills are indentations (small pyramid shapes) designed to break the paper fibers on stamps so that the ink from a cancellation would soak into the stamp more, making it more difficult to remove cancels and reuse stamps.
Grills come in two forms: female grills and male grills.
Female grills were made by a roller which made indentations so that the stamp paper was pressed into the roller. From the front of the stamp, female grills point upwards towards you. Male grills are made by rollers which had sharp points that pressed into the paper. From the front of the stamp, male grills point downwards.
There are 9 different grills. They are designated with capital letters. Their sizes are given by counting the number of points in the grill. The horizontal dimension is given first, then the vertical dimension. Why the different sizes? The USPOD and the Bureau of Engraving and Printing (BEP) experimented with different sizes trying to find a grill large enough that it would soak up the ink from the cancel, but small enough that it didn’t interfere with the production and distribution of the stamps.
Grills were used from about 1867-1870. Seven trills were used on the 1861 issues:
The A (female) grill covers the entire stamp. It interfered with the perforations. It’s very difficult to find any stamps with an A grill that have nice perforations. These are Scott #79-81. Scott #79 is obtainable. Scott #80 (4 copies) and #81 (8 copies) are very rare.
The B (female) grill measures 22 by 18 points. This is Scott #82 and only 4 copies are known.
The C (female) grill is 16 to 17 by 18 to 21 points. It is Scott #83 and is scarce.
The D (male) grill is 15 by 17 to 18 points. This is Scott #84 and #85. Both are scarce, but obtainable.
The Z (male) grill is 13 to 14 by 18 points.Scott #85A is rare (2 copies known). Scott #85B, #85C, and #85E are obtainable. Scott #85D (6 copies) and #85F (2 copies) are very rare.
The E (male) grill is 14 by 15 to 17 points. This is Scott #86 to #91.
The F (male) grill is 11 to 12 by 15 to 17 points. This is Scott #92 to #101.
The E and F grills are the most common and most Scott numbers are obtainable.
The G grill is 12 by 11 points and was only used on the 1869 pictorials, Scott #112 to 122.
The H (11 to 13 by 14 to 16 points) and I grills (10 to 11 by 10 to 13 points) were used on the 1870-71 large banknotes, Scott #134 to #144. Again, these are generally obtainable.
“United States Grills and Notes on the Grilled Issues of the U.S.” by Stevenson and Brookman is an excellent reference for understanding grilled stamps. Beware, fakes are known of grilled stamps, especially on the more rare stamps.