They include a 12-inch wide Viennese dish described as "one of the most important examples of early Viennese porcelain in the British Museum collection".
The other is a "monteith", a bowl filled with water used to cool glasses, held at Cambridge University's Fitzwilliam Museum since 1960.
However, the former will not be returned to its rightful owner because of a 1963 law prohibiting national museums from disposing of their collections - no matter how they were acquired.
In 1938 the Gestapo forced her uncle, a Jewish businessman called Heinrich Rothberger who owned a large Vienna department store, to sell his large porcelain collection.
He used the money to pay the swingeing taxes the Nazis imposed to bankrupt Jewish businesses. He then fled with his wife Ella to Canada.
The British Museum stressed it put in much of the detective work to track down Bertha Gutmann, after it discovered the piece's dark history.
In 2005 the High Court ruled no item could be returned or "restituted" to its rightful owner, even if it had been looted, without changing the British Museum Act (1963).
The Government-appointed Spoliation Advisory Panel, which made Wednesday's ruling on the two items, expressed its disappointment that the law remained unchanged.
It stated: "We expect that, had restitution been available, the claimant would have sought it, as she has done in the Fitzwilliam Museum case."
The panel recommended five years ago that the law been changed, it said, adding "so far as we can judge, is not likely to be in the near future".
Margaret Hodge, the culture minister, responded: "Although the claimant has said they are happy with the outcome, this case illustrates the paradox in the present system where historic legislation prevents a consistent approach from all museums in responding to claims.
"This is something that the Government will want to seriously consider going forward."
The Viennese dish came into the British Museum's collection in 1939, having been presented by an employee called William King.
Although it is not known how he acquired it, the panel said he "knew the Rothberger collection and might have seen it in Vienna."
Even though he probably knew of the forced sale a year earlier, the panel concluded that the British Museum had acquired it "in good faith".
It said: "Nowadays, it would be a standard precaution to investigate its provenance at the time of acquisition, but this was far from being the universal practice in 1939 and we do not criticise the British Museum for not having done so at that time."
The monteith was bequeathed to the Fitzwilliam Museum in 1960 by Louis Clarke, who was director there from 1937 to 1946. Similar items have sold recently at auction for £10,000 to £15,000.
The panel found the museum was "understaffed" in 1960 and should not "be criticised for failing to establish, at the time of acquisition, the provenance of this one item from this enormous collection."