We have all the potential for a good plot here. A young noblewoman bucks expectations in failing to get busy and reproduce. Not only that, but she's a Christian in a pagan city. We smell trouble.
This definitely represents a conflict for the Christians in the tale, who must either betray their faith or lose their heads. Cecilia's husband Valerian and brother-in-law Tiburtius choose death. For them, it is an easy decision, for as Cecilia has taught them, there's another life on the other side. In fact, the Christians' relative lack of interest in their earthly life when it's compared with eternal life with God means that for them, this choice is actually not much of a conflict at all. But it'll do for our purposes.
Rather than simply declaring "Off with her head!" when Cecilia refuses to worship at the shrine of Jupiter, Almachius anticipates her refusal, and he wants to know the reason why. So he orders Cecilia to be brought before him before she's taken to the shrine, a definite break with tradition, and a definite complication for our heroine.
Here we have the climactic confrontation between pagan oppressor and virgin martyr. This is what both the story and Cecilia's life have been leading up to all along. Cecilia has the opportunity to defend her faith in a public venue, perhaps winning converts in the process, but certainly demolishing the arguments of the biggest symbol of paganism.
Although based on everything that's come before this moment we're pretty sure we know what Cecilia will choose, this could be a suspenseful moment. After all, this is Cecilia's ultimate test: will she stick to her principles, or will she bow before that most persuasive of arguments, death?
Well, here's the result of Almachius's ultimatum: a half-dead Cecilia who preaches and teaches continually. We sense that this is the denouement because we suspect that Cecilia won't remain alive for much longer. Maybe it's the head dangling from her body, or maybe it's because Cecilia's doing estate planning, but we get the feeling her life is drawing toward its conclusion.
This being a virgin martyr legend, this ending is exactly the one we were expecting. The sanctifying of Cecilia's home as a church ensures that her legacy will live on in her shrine and in the legend that will grow up around it.