Tony is telling Hastings that if something belongs to you, you can always take it.
By saying “An honest man may rob himself of his own at any time,” Tony is referring to the fact that the jewels Miss Neville has belong to her, so she might as well run off with them. She will not be breaking the law, she will be stealing from herself.
Mrs. Hardcastle tells Miss Neville not to bother with jewels, because she won’t need them until her beauty leaves her much later in life. She says the jewels have been lost so she won’t have to give them to Miss Neville, but then finds out they are actually missing.
MRS. HARDCASTLE. Don't be alarmed, Constance. If they be lost, I must restore an equivalent. But my son knows they are missing, and not to be found.
Of course, Tony is not the honest one because he is the one who stole the jewels in the first place! He is keeping them so that he doesn't have to marry Miss Neville! After all, they are his, so he is not really robbing himself and because he is an honest man he can rob himself!