There is no H49 Ithaca. There is a M49, made for 17 years, single shot 22 cal worth $75 to $100. There is also a M49R, 22 cal repeater, tube fed. Made for 3 years worth $ 250 and more, sonetime much more.
1942
Ithica m49 price guide
The Model 37 was mfg. in 1956. The -4 indicates FULL choke.
What is the condition of the gun and the barrel length?
I think what you have is a model 49. Get out the magnifying glass and take another look.
Historical Overview of the Ithaca Gun Co. says that in 1987 Ithaca Acquisitions, Inc. Moved the gun making operations to King Ferry, NY. and changed the model m-37 to model 87. In 1996 Ihtaca gun Co. LLC changed it back to model 37.
1975
this is a Lewis model made between 1905 1910.
You have an Ithaca sxs Miner model made 1907.
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.
Depends entirely on age and condition - neither of which is indicated in the question, so no way to answer.
1956.....#'s 602,000-652,000 were produced in 1956.