Now the good news Gerret :D http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GRid=83315416
There is a lot of info at WikiTree on your ancestor already :D http://www.wikitree.com/wiki/Space:Van_Swearingen_and_Children%2C_A_Family_History
Here his profile with --- I m sure ----- some things not totally right :D http://www.wikitree.com/wiki/Van_Swearingen-50 But we can change that! Please if you find the grave, and I really hope so for you, please make some pictures to add to his profile. Thank you!
Oh BTW add Dutch_Roots tags to your posts here. So the members of the Dutch Project will see your message and help you where ever they can! :D
This is my ancestor too - hello cousin Gerret. Here's the New Netherland Settlers project profile http://www.wikitree.com/wiki/Van_Swearingen-14
I could swear that I "Dutchyfied" his first name at some point but I don't think I made it "Gerrett". It should be "Gerrit van Sweringen" but there are definitely a lot of chefs for that soup, if you know what I mean. van Swearingen and later just Swearingen are the Americanisms.
It is well known among official researchers of the family that "Beemsterdam" is a made-up place, but I don't remember if the real place of origin was determined.
The most pervasive story seems to be that Gerrit was buried under the floor of the St. Mary's City Chapel
http://www.hsmcdigshistory.org/research/history/garrett-van-sweringen/