There are a number of general interest collectors publications in newspaper format full of classified ads.  Ads in such publications will tend not to bring in many qualified buyers.  You can usually find copies of these publications at your local large antiques mall.

 Selling off piece-by-piece…

If the family is in no particular hurry to sell the estate items and do not mind multiple visits from prospective buyers, you can sell piece-by-piece.  This could be a good way to sell off the more desirable parts of the collection at a market price but you are likely to wind up with a lot of unsold items of lesser quality.  You would probably have to negotiate a lot price for the remainder at a fraction of the market price.

If someone in the family wishes to take on the task; in every region there are groups of vintage radio enthusiasts that organize events that include some sort of flea market where you can sell the items.  These events can attract anywhere from 50 to over a thousand qualified collectors.  Amateur radio clubs also sponsor “hamfests” which are primarily flea markets of all kinds of electronic products.  These events attract anywhere from a few hundred to several thousand folks.  There will not likely be a large number of enthusiastic collectors at hamfests but you may have the opportunity to meet people that might be looking for just one old radio “like my grandmother had in the front parlor”.

 Selling off as a lot…

There are a number of folks in the hobby that are willing to purchase an entire collection.  Some are simply running a business that cater to the hobby and others are collectors that are willing to buy the whole collection as a way of getting first-choice for their collection…. They usually dispose of the remainder of items piece-by-piece at the various vintage radio gatherings or via Internet sales or magazine advertisements.
The advantage of such a deal is that all of the items are disposed of at one time … the good stuff as well as the dregs …  in a matter of weeks.  The down side is that you are likely to yield less money for the collection than by other means.  Most likely in the range of 40 to 70 cents on the dollar.

 Holding an on-site auction….

In my opinion this is a good option only if the collection is large and desirable enough to attract buyers from a large area.   Most auctioneers will have not had experience in selling off such merchandise and will need consultation from your advisor.  It will be absolutely necessary to advertise in national and regional collector publications and place notices on web sites.  If the sale is only advertised in local newspapers it is likely that only a small number of qualified/enthusiastic buyers will be at your sale.  The auction professionals that I know usually require 25 to 40 % of gross sales for their services.  There are a small number of auctioneers that have had specific experience in selling vintage radio collections and their advertisements can be found in Antique Radio Classified.