Re: What scope base for Remington Mod. 37 (Rangemaster
First congrats on finding this great rifle. First you have to make several decisions. What type of scope do you want to put on the rifle. By that I mean do you want a vintage scope, ie unertl, or Redfield 3200; or do you want a modern scope. If you want a vintage scope they can cost any where from $500 to 1500. They were made to fit on the barrel mounts, which you are missing, but are easily available.
Now if you want to put on a modern scope, again there are choices on how to mount it. You can have the receiver drilled and tapped for a modern scope mount. The draw back to this approach is that you will lose $100 dollars in value for every hole added to the receiver as a collector rifle. It is your rifle and you can of course do as you please with it.
There is an alternative option that is described in the following article:
http://www.jmtpublishing.com/articles/2012/Scoping_Barrel_Block_Rifle_New_base_Mount.asp
That seems like a good approach. Personally since I have several vintage target rifles I am planning to purchase one or two vintage scopes and use them on the various rifles. My second choice would be follow the instructions from the above article.
There is one other possibility that is to call EGW, and see if their cantilever scope mount for the Win 52/Kimber 82G will also work for the M-37.
Hope this helps steer you in the right direction
Don
PS I forgot to mention the the bolt handle has an unusually high throw which means modern scope selection and ring height must be made with this in mind.