A professionally prepared "Appraisal" by an accredited/certified Appraiser ( like what you might need for an CRA - Official Tax Receipt for a GIK Donation to a charity ) can be a little expensive ... an "Opinion of Value" is another matter - and the credentials or bona fides of the valuer may come into play.
"Value" can mean several different things ... like an average retail market value, replacement value required for insurance, a person-to-person private transaction value or trade-in value, for example ... all vary in amount for the same firearm.
The Blue Book of Gun Values is likely as good a guideline as any, provided the values are taken withing ther context of what country you're in and regional differences for the value of certain firearms. For example, I see lots of retail ads for example, for a shotgun like the little Browning 20 gauge (BSS) SxS's in the States for $ 2250 - $ 2500. Up here,
$ 1500- $ 2000 might seem a little more reasonable, while I've bought and run into a couple more for as little as $ 800, to as much as $ 1500 privately. Very good to Excellent condition collectable pre-64 Winchesters ( like Mod.s 12, 21, 42, 70, 18886, 1892, 1894. 71 etc.) inavariably seem to bring more ... to a lot more... money in the US.
An experienced dealer in an established well-respected retail setting may be able to provide you with a written opinion of value sufficient for what you require.