Princess Karoline Arenberg by Moritz Michael Daffinger (auctioned)
Christie's has this about the portrait: "MORITZ MICHAEL DAFFINGER (AUSTRIAN, 1790-1849)Princess Karoline Arenberg (1801-1875), in lace-bordered white silk dress with voluminous sleeves, white belt with gold buckle, gold-set carnelian and drop-pearl pendant at corsage, fur stole draped over her right shoulder, her light brown hair upswept and dressed in ringlets and adorned with pink rose and foliage: draped red curtain and sky and cloud background.
Rectangular, 4 x 3 1/16 in. (102 x 78 mm.), gilt-metal easel frame with foliate corners, the reverse engraved 'Princessin Karoline Arenberg verwittwete Fürstin Starhemberg geb. Gräfin Kaunitz Rietberg geb. 27 Mai 1801 gestorb. 18 Juni 1875 in Wien.', fitted hinged red leather case..."
The Wikipedia article about the Belgian Arenberg family is here.