Penalized function-on-function regression, as implemented in the R package refund, considers all grid values as independent conditional on the linear predictor, but some dependence typically remains. We study the consequences for estimates and pointwise intervals in a simulation and a plasmode study on nine real datasets. Under dependence, restricted maximum likelihood (REML) undersmooths the coefficient surface: in our simulations' main settings, its relative error is two to four times that of curve-blocked neighborhood cross-validation (NCV). In our plasmode study, both fits have large errors, possibly through weak identification, and NCV is usually, but not always, better. Under dependence, the independence-model-based intervals for means and surfaces undercover severely. We propose and evaluate a curve-clustered sandwich covariance with a leverage adjustment for the penalized hat matrix with Satterthwaite degrees of freedom which brings coverage close to nominal in most settings. Its intervals for function-on-function effects are wide because REML's estimate is noisy. The same construction at the NCV estimate is narrow but undercovers. We therefore recommend fitting twice: NCV for the shape of the surface, REML with these intervals for inference. For estimated means, intercept functions and scalar covariate effects, one REML fit with these intervals usually suffices.

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