The duchess of Lorraine (Christina of Denmark) had a daughter, Dorothea, who married Eric, duke of Brunswick-Calenburg. Likewise, Wilhelm V of Brunswick-Luneburg married Dorothea of Denmark, (youngest) daughter of the Danish king (can't remember which Frederik or Christian it was though).
Also, the OTL wife of George I was originally proposed as a marriage partner to the crown prince of Denmark according to one biography I read on George I. Sophia, in spite of being against George marrying her (and the lady likewise), spread rumors that the marriage did not come off, and also removed a possible marriage to the prince of Brunswick-Wolfenbuttel so that George I could marry her (who, when Sophie Dorothea heard of this, she declared "I will not marry the pig-snout" and promptly fainted.)
As to Danish kings without heirs, Christian IV is a good example - eldest and second (legitimate) son predeceased him without issue, Frederik III was his third son. He was married to a Hannoverian princess, too. Then the Danish succession crisis in the 19th century also came from kings who either had no male heirs, or male heirs that were unable to have children (because their wives were barren/they had bad relationships).