The Swale Baronetcy created in 1660 is presumed to have become extinct in the 1700s on the death of the 4th Baronet.
Nevertheless it was claimed from 1877 by persons claiming to be descended from the fourth son of the 1st Baronet.
A Sir James Swale, 10th Bt., is included in Dod's 1904 Peerage, page 869, though the entry says that the title "is not admitted by the Officers of Arms":
https://www.google.com/books/edition/Dod_s_Peerage_Baronetage_and_Knightage_o/CpkfAQAAMAAJ?hl=en&gbpv=1Cokayne has pointed out that the claimed descent is unproved and suspect.
Even though this is likely a false claim (and certainly an unproved one), I thought it would be interesting to see that the claim continued well into the 1900s. Here is a burial record for "Sir James Bishop Swale", who died 4 October 1949:
https://www.findagrave.com/memorial/99083220/james-bishop-swaleAn obituary from the Bedford Advertiser, 6 Oct 1949, is pasted onto the page:
"SIR JAMES BISHOP SWALE, of Rudfarlington, Plumpton, near Harrogate who has died at the age of 81, was the holder of a baronetcy that had no claimant for nearly 150 years.
I"t was held at various times by a parson, a publican and an ironmonger.
"The first baronet, Solomon Swale was Member of Parliament for Aldborough near Boroughbridge and received the title from Charles II.
"He was succeeded by another Solomon who died in 1732 almost penniless and until 1877 there was no claimant.
"Curious History.
"Then the Rev John Swale of Birtley, Co. Durham, a brother of the Order of St Benedict, successfully claimed the title, not, as he said at the time, for personal gain, but for the future welfare of an ancient house.
"Ten years later another John Swale, landlord of the Royal Oak Inn, Knaresborough succeeded to the baronetcy and became known as the 'landlord baronet'.
"Within a few months he died and the title went to a near relative, Benjamin Swale who was an ironmonger in Knaresborough.
"It was from him in 1888 that James Bishop Swale, farmer, inherited the baronetcy. But he preferred to be known both in his private and business life as plain 'Mr'. He is succeeded by his son Mr James Bernard Swale, who will be the twelfth baronet"
The Findagrave page lists one son, James Bernard Swale, said to have died in 1965.
https://www.findagrave.com/memorial/99083221/james_bernard-swale