I looked at the USS Constellation 1797 photos on line and she does show 13 gun ports on each side today. I was surprised as this is not what she had when launched or during the Barbary Wars 1801 -1805. She was a nominally rated 38-gun frigate, but the actual number and type of guns, and thus gunports, varied. As it turns out 13 or 14 or 15 per side could be right depending on what year she is depicted.
From the little searching I did, the following is interesting.
A quarter bill from 1812 assigned a crew to 14 of the ship's 15 gundeck guns per side.
A model created in late 1812 by members of the crew shows the ship with what appeared to be 15 ports on each side at the gundeck level.
The ship's current configuration, following the 1927-1931 restoration, has a total of 30 guns on the gundeck, consisting of 18 long guns and 12 short guns.
The most recent restorations have her 13 per side.
From the Naval Institute:
During the War of 1812, her armament consisted of 2 long 32's, 24 long 18's, (13 per side??) and eighteen 32-pdr. carronades. In 1819, this was increased by the addition of 4 more 18-pdr. In October, 1840, she rated 30 long 18's and sixteen 32-pdr. carronades
Lots of choices, all of which are correct depending on the time period.
Allan