Made in 1899. Value will depend a lot on the condition of the gun, how tightly it locks up, whether there are any cracks in the wood, the "patina" of the barrels, etc. If in very good condition it would probably bring between $350 and $500. Every now and then a similar gun will be sold at www.gunbroker.com, and you could get a better idea of current value by watching those listings.
With the serial number that you provided,your Ithaca double barrel shotgun with the damascus barrels was produced in the year 1900.
Ithaca SN 68814 was manufactured in 1902 according to Ithaca Gun Company records compiled and released in 1960. It is a Lewis model if hammerless and New Ithaca Gun if it has hammers.
It is only worth what the person buys it for...
http://www.gunshop.com/dgsnos3.htm
$317
this is a Lewis model made between 1905 1910.
It is a 10 gauge if it has a damascus barrel and it in mint condition can be worth up to 2000 bucks
I am not sure about the age or value, but I would sure like to own it to rabbit hunt with.
This should be a Lewis model, made in 1902.
You don't.
It sounds to me like you have a Early made Ithaca Baker model double barrel shotgun made in 1889-1890.As to value I would have someone with the knowledge to evaluate you gun and then he could assign a value for you.
The guage and grade of an Ithaca Hammerless can generally be found on the left front corner of the water table on the frame. The serial number is usually on the right side of the same water table, on the barrel flats, and on the forend iron. To determine which design you have, check http://www.shotgunworld.com/identify.html