Note the question mark at the end there. I'm asking for your help. As I see it, there are not really a lot of contenders, so here's a rundown:
Superman and Lois Lane: A rather tepid romance at best, and it was not, as Mort Weisinger put it, consummated during the Silver Age (although that changed eventually).
Batman and ???: 'Nuff said.
Barry Allen and Iris West. One of several marriages within the Silver Age of a long-dating couple. Lots of good interaction, although Iris could be a beeyatch when she wanted to as well.
Aquaman and Mera. One of the definitely consummated marriages in the Silver Age; they did, after all, have a son.
Green Lantern/Hal Jordan and Carol Ferris. It ended badly, and this was always an oddball romantic triangle with Hal competing against his secret identity as I have discussed previously.
Ray Palmer and Jean Loring. A solid contender; don't let the ridiculous Identity Crisis storyline distract you. A major reason why Ray fought crime as the Atom was to help Jean establish her practice so she'd marry him.
Hawkman and Hawkgirl: Unique situation as the Halls were married when we first met them. Worked well together both in their costumed identities and as civilians.
Ralph Dibney and Sue Dibney: Another early married couple, one of the charms of the Detective Comics series was the interaaction between the pair.
Reed Richards and Sue Storm. Another rare case of consummated love, as they bore a son as well in the Silver Age.
Peter Parker and Gwen Stacy. Ill-fated and frequently tested, their love was surprisingly strong during the late 1960s.
Hank Pym and Janet Van Dyne. Like the Dibney's they were not really major characters at the time, but they did marry.
Bruce Banner and Betty Ross. They came close to getting married in the Silver Age, but I never really felt a strong bond between the two.
Any others? The Marvel characters pretty much turned over all their girlfriends before the decade was over: Karen Page, Jane Foster, Pepper Potts, etc. Archie and Veronica/Betty and Richie Rich/Gloria are cute, but not really romance in my book.
Update: Some very good suggestions in the comments:
Adam Strange and Alanna. An excellent romance with lots of interaction, the involuntary separations and even an accepted proposal of marriage. A very strong contender.
Ben Grimm and Alicia. If we look at a romance as union of yin and yang, this would have to rate strongly. Alicia completes Ben, and softens his hard edges (although figuratively, not literally).
Green Arrow and Black Canary. I'd rate this as more of a Bronze Age Romance. Same with the Vision and the Scarlet Witch.
Catwoman and Batman. Terrific pick but more Golden Age than Silver; the Catwoman only made two real appearances in Batman during the Silver Age.
BTW, on the consummated part, I do think that marriage and children are an important manifestation of love, but I was also being a little puckish; see this post for more.