This really depends upon where in Europe you are located.

If you are English there is a good chance you will be able to claim the dowry you brought with you into the marriage that had been managed by your husband until his death. It was therefore possible for you to remarry, and use the resources you possessed to make yourself an attractive match. Barbara Hanawalt notes that since widows were no longer under the control of their fathers or husbands they could, if favourable conditions permitted, become quite independent. Hanawalt, The Wealth of Wives: Women, Law and the Economy in Late Medieval London (Oxford: OUP, 2007), 104.

Hanawalt believes contemporaries viewed them on occasion as "sexually aggressive," which perhaps simply meant that some people were shocked that these women had the daring to exercise meaningful agency over their amorous and sexual futures.

"Neighbours and friends expected the widow to wail and lament her loss...but the widow was not supposed to make excessive show of mourning because that made others uncomfortable. She was expected to bury her husband, see that his will was executed and prepare to live a chaste life while rearing children and looking after her household." (Ibid, 105.)

It Italy this was more complicated, and in Florence for example the dowry would be retained within the "paternal estate" in order to support those children sired by the deceased husband. Women wishing to remarry would therefore have to find additional resources to provide a new dowry for any remarriage that might occur. David Herlihy has observed that women who remarried frequently did not bring their children with them from the previous marriage; they remained in the care of her dead husband's relatives. David Herlihy, Medieval Households (Cambridge: Harvard University Press, 1985), 153.

In France, depending upon the regional locality, you could expect to retain control over your dowry and also over the "dower" which was provided by your husband. This dower offered additional "lands, revenues and moveable property" that your could make claims upon following your husband's death. These might be challenged in court but you would have a claim nonetheless. Theodore Evergates has provided examples from Chartrain where women were able to hold onto these assets and even bring them into new marriages. Theodore Evergates, *Aristocratic Some in Medieval France" (Philadelphia: University of Pennsylvania Press, 1999), 54.

Jennifer Ward has also shown that siblings often kept in contact with one another throughout their lives. It was not uncommon for siblings to name one another as executors in their wills or to ask them for financial assistance if they fell upon hard times. Jennifer Ward, Women in England in the Middle Ages (London: Hambledon, 2006), 76. You could therefore have a reasonably large kinship network from which you could draw assistance and resources. They may in fact have information regarding potential suitors that could benefit you before long. It really depends on a large number of factors that are not easily reducible to a few paragraphs.

Hopefully this helps a little bit nonetheless.