Here is the inscription spelled out with all abbreviations expanded, ligatures spelled separately, and V spelled as U when it stands for a vowel:
Nobilissimae ac Pientissimae
Dominae Elisabethae Szuditth
Consorti Dilectissimae Sibi
Suisque Posteris Generosus
Dominus Ioannes Logmagi de
Raguseo Poni Curavit
The vocabulary is pretty standard apart from the names and piens instead of the more common pius.
Perhaps this variant was used to get a less awkward superlative.
Please bear in mind that Latin superlatives don't work quite like the English ones, and e.g. "most beloved" below should be understood as "dearly/very/highly beloved".
You can use superlatives like this in English as well, but it is far less common than in Latin.
This could be translated as follows, line by line:
To the most noble and most dutiful
lady Elisabeth Judith,
to the most beloved partner to him
and to his descendants, the generous
mister John Logmagi
of Dubrovnik had [this stone] put in place
in the year 1620
Dubrovnik is known as Ragusium or Ragusa in Latin, and this inscription suggests the (unsurprising) variant Raguseum.
I am unsure whether sibi suisque posteris should modify dilectissimae or generosus.
Either Elisabeth was loved to John and his family or John was generous to himself and his family.
Either would make sense, but I chose the first option.